Analysis and applications: The mathematical work of Elias Stein

Fefferman, Charles; Ionescu, Alex; Tao, Terence; Wainger, Stephen

doi:10.1090/bull/1691

Analysis and applications: The mathematical work of Elias Stein
HTML articles powered by AMS MathViewer

by Charles Fefferman, Alex Ionescu, Terence Tao and Stephen Wainger; with contributions from Loredana Lanzani; with contributions from Akos Magyar; with contributions from Mariusz Mirek; with contributions from Alexander Nagel; with contributions from D. H. Phong; with contributions from Lillian Pierce; with contributions from Fulvio Ricci; with contributions from Christopher Sogge; with contributions from Brian Street HTML | PDF

Bull. Amer. Math. Soc. 57 (2020), 523-594 Request permission

Abstract:

This article discusses some of Elias M. Stein’s seminal contributions to analysis.

References

J. M. Aldaz, The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension, Ann. of Math. (2) 173 (2011), no. 2, 1013–1023. MR 2776368, DOI 10.4007/annals.2011.173.2.10
David E. Barrett, Behavior of the Bergman projection on the Diederich-Fornæss worm, Acta Math. 168 (1992), no. 1-2, 1–10. MR 1149863, DOI 10.1007/BF02392975
David E. Barrett and Loredana Lanzani, The spectrum of the Leray transform for convex Reinhardt domains in $\Bbb C^2$, J. Funct. Anal. 257 (2009), no. 9, 2780–2819. MR 2559717, DOI 10.1016/j.jfa.2009.04.011
Michael Beals, Charles Fefferman, and Robert Grossman, Strictly pseudoconvex domains in $\textbf {C}^{n}$, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 2, 125–322. MR 684898, DOI 10.1090/S0273-0979-1983-15087-5
V. Bergelson and A. Leibman, A nilpotent Roth theorem, Invent. Math. 147 (2002), no. 2, 429–470. MR 1881925, DOI 10.1007/s002220100179
J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85. MR 874045, DOI 10.1007/BF02792533
J. Bourgain, On high-dimensional maximal functions associated to convex bodies, Amer. J. Math. 108 (1986), no. 6, 1467–1476. MR 868898, DOI 10.2307/2374532
J. Bourgain, On the $L^p$-bounds for maximal functions associated to convex bodies in $\textbf {R}^n$, Israel J. Math. 54 (1986), no. 3, 257–265. MR 853451, DOI 10.1007/BF02764955
J. Bourgain, On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math. 61 (1988), no. 1, 39–72. MR 937581, DOI 10.1007/BF02776301
J. Bourgain, On the pointwise ergodic theorem on $L^p$ for arithmetic sets, Israel J. Math. 61 (1988), no. 1, 73–84. MR 937582, DOI 10.1007/BF02776302
J. Bourgain, A remark on the maximal function associated to an analytic vector field, Analysis at Urbana, Vol. I (Urbana, IL, 1986–1987) London Math. Soc. Lecture Note Ser., vol. 137, Cambridge Univ. Press, Cambridge, 1989, pp. 111–132. MR 1009171
Jean Bourgain, Pointwise ergodic theorems for arithmetic sets, Inst. Hautes Études Sci. Publ. Math. 69 (1989), 5–45. With an appendix by the author, Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein. MR 1019960
Jean Bourgain, Some new estimates on oscillatory integrals, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991) Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 83–112. MR 1315543
Jean Bourgain, On the Hardy-Littlewood maximal function for the cube, Israel J. Math. 203 (2014), no. 1, 275–293. MR 3273441, DOI 10.1007/s11856-014-1059-2
Jean Bourgain and Ciprian Demeter, The proof of the $l^2$ decoupling conjecture, Ann. of Math. (2) 182 (2015), no. 1, 351–389. MR 3374964, DOI 10.4007/annals.2015.182.1.9
Jean Bourgain, Ciprian Demeter, and Larry Guth, Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three, Ann. of Math. (2) 184 (2016), no. 2, 633–682. MR 3548534, DOI 10.4007/annals.2016.184.2.7
D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class $H^{p}$, Trans. Amer. Math. Soc. 157 (1971), 137–153. MR 274767, DOI 10.1090/S0002-9947-1971-0274767-6
S. Buschenhenke, S. Dendrinos, I. Ikromov, and D. Müller, Estimates for maximal functions associated to hypersurfaces in ${\mathbb {R}}^3$ with height $h<2$, Part I, arXiv:1704.06520 (2017).
A.-P. Calderón, Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092–1099. MR 177312, DOI 10.1073/pnas.53.5.1092
A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
A.-P. Calderón and A. Zygmund, On higher gradients of harmonic functions, Studia Math. 24 (1964), 211–226. MR 167631, DOI 10.4064/sm-24-2-211-226
Anthony Carbery, An almost-orthogonality principle with applications to maximal functions associated to convex bodies, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 269–273. MR 828824, DOI 10.1090/S0273-0979-1986-15436-4
Anthony Carbery, Michael Christ, and James Wright, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (1999), no. 4, 981–1015. MR 1683156, DOI 10.1090/S0894-0347-99-00309-4
Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 199631, DOI 10.1007/BF02392815
Michael Christ, Hilbert transforms along curves. I. Nilpotent groups, Ann. of Math. (2) 122 (1985), no. 3, 575–596. MR 819558, DOI 10.2307/1971330
Michael Christ, Pointwise estimates for the relative fundamental solution of $\overline \partial _b$, Proc. Amer. Math. Soc. 104 (1988), no. 3, 787–792. MR 929407, DOI 10.1090/S0002-9939-1988-0929407-5
Michael Christ, Regularity properties of the $\overline \partial _b$ equation on weakly pseudoconvex CR manifolds of dimension $3$, J. Amer. Math. Soc. 1 (1988), no. 3, 587–646. MR 928903, DOI 10.1090/S0894-0347-1988-0928903-2
Mike Christ, On the $\overline \partial _b$ equation and Szegő projection on CR manifolds, Harmonic analysis and partial differential equations (El Escorial, 1987) Lecture Notes in Math., vol. 1384, Springer, Berlin, 1989, pp. 146–158. MR 1013821, DOI 10.1007/BFb0086799
Michael Christ, A $T(b)$ theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990), no. 2, 601–628. MR 1096400, DOI 10.4064/cm-60-61-2-601-628
Michael Christ, On the $\overline \partial _b$ equation for three-dimensional CR manifolds, Several complex variables and complex geometry, Part 3 (Santa Cruz, CA, 1989) Proc. Sympos. Pure Math., vol. 52, Amer. Math. Soc., Providence, RI, 1991, pp. 63–82. MR 1128584
Michael Christ, The strong maximal function on a nilpotent group, Trans. Amer. Math. Soc. 331 (1992), no. 1, 1–13. MR 1104197, DOI 10.1090/S0002-9947-1992-1104197-X
R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170
Tristan C. Collins, Allan Greenleaf, and Malabika Pramanik, A multi-dimensional resolution of singularities with applications to analysis, Amer. J. Math. 135 (2013), no. 5, 1179–1252. MR 3117305, DOI 10.1353/ajm.2013.0042
Mischa Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105–167 (1956) (English, with Spanish summary). MR 84632
Michael Cowling, The Kunze-Stein phenomenon, Ann. of Math. (2) 107 (1978), no. 2, 209–234. MR 507240, DOI 10.2307/1971142
Guy David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 1, 157–189 (French). MR 744071
L. Deleaval, O. Guédon, and B. Maurey, Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets, arXiv:1602.02015 (2016).
L. Ehrenpreis and F. I. Mautner, Uniformly bounded representations of groups, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 231–233. MR 71434, DOI 10.1073/pnas.41.4.231
Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36. MR 257819, DOI 10.1007/BF02394567
Charles Fefferman, The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330–336. MR 296602, DOI 10.2307/1970864
Charles Fefferman, A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52. MR 320624, DOI 10.1007/BF02771772
Charles Fefferman, Pointwise convergence of Fourier series, Ann. of Math. (2) 98 (1973), 551–571. MR 340926, DOI 10.2307/1970917
Charles Fefferman, Parabolic invariant theory in complex analysis, Adv. in Math. 31 (1979), no. 2, 131–262. MR 526424, DOI 10.1016/0001-8708(79)90025-2
Charles Fefferman, Selected theorems by Eli Stein, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991) Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 1–35. MR 1315540
C. L. Fefferman and J. J. Kohn, Estimates of kernels on three-dimensional CR manifolds, Rev. Mat. Iberoamericana 4 (1988), no. 3-4, 355–405. MR 1048582, DOI 10.4171/RMI/78
Charles L. Fefferman and Joseph J. Kohn, Hölder estimates on domains of complex dimension two and on three-dimensional CR manifolds, Adv. in Math. 69 (1988), no. 2, 223–303. MR 946264, DOI 10.1016/0001-8708(88)90002-3
C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 590–606. MR 730094
Charles L. Fefferman and Antonio Sánchez-Calle, Fundamental solutions for second order subelliptic operators, Ann. of Math. (2) 124 (1986), no. 2, 247–272. MR 855295, DOI 10.2307/1971278
I. M. Gelfand and M. A. Neumark, Unitäre Darstellungen der klassischen Gruppen, Akademie-Verlag, Berlin, 1957 (German). MR 0085262
V. Guillemin and G. Uhlmann, Oscillatory integrals with singular symbols, Duke Math. J. 48 (1981), no. 1, 251–267. MR 610185
Michael Greenblatt, Sharp $L^2$ estimates for one-dimensional oscillatory integral operators with $C^\infty$ phase, Amer. J. Math. 127 (2005), no. 3, 659–695. MR 2141648
Allan Greenleaf, Malabika Pramanik, and Wan Tang, Oscillatory integral operators with homogeneous polynomial phases in several variables, J. Funct. Anal. 244 (2007), no. 2, 444–487. MR 2297031, DOI 10.1016/j.jfa.2006.11.005
Allan Greenleaf and Andreas Seeger, Oscillatory and Fourier integral operators with degenerate canonical relations, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), 2002, pp. 93–141. MR 1964817, DOI 10.5565/PUBLMAT_{E}sco02_{0}5
Allan Greenleaf and Andreas Seeger, Oscillatory integral operators with low-order degeneracies, Duke Math. J. 112 (2002), no. 3, 397–420. MR 1896469, DOI 10.1215/S0012-9074-02-11231-9
Allan Greenleaf and Gunther Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Funct. Anal. 89 (1990), no. 1, 202–232. MR 1040963, DOI 10.1016/0022-1236(90)90011-9
Philip T. Gressman, Uniform estimates for cubic oscillatory integrals, Indiana Univ. Math. J. 57 (2008), no. 7, 3419–3442. MR 2492238, DOI 10.1512/iumj.2008.57.3403
Philip T. Gressman and Lechao Xiao, Maximal decay inequalities for trilinear oscillatory integrals of convolution type, J. Funct. Anal. 271 (2016), no. 12, 3695–3726. MR 3558254, DOI 10.1016/j.jfa.2016.09.003
S. Guo, J. Roos, and P.-L. Yung, Sharp variation-norm estimates for oscillatory integrals related to Carleson’s theorem, arXiv:1710.10988 (2017).
Shaoming Guo, Lillian B. Pierce, Joris Roos, and Po-Lam Yung, Polynomial Carleson operators along monomial curves in the plane, J. Geom. Anal. 27 (2017), no. 4, 2977–3012. MR 3708001, DOI 10.1007/s12220-017-9790-7
G. M. Henkin, Integral representation of functions which are holomorphic in strictly pseudoconvex regions, and some applications, Mat. Sb. (N.S.) 78 (120) (1969), 611–632 (Russian). MR 0249660
Carl S. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 996–999. MR 63477, DOI 10.1073/pnas.40.10.996
I. I. Hirschman Jr., On multiplier transformations, Duke Math. J. 26 (1959), 221–242. MR 104973
I. I. Hirschman Jr., Multiplier transformations. II, Duke Math. J. 28 (1961), 45–56. MR 124693
Lars Hörmander, Notions of convexity, Progress in Mathematics, vol. 127, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1301332
Kevin Hughes, The discrete spherical averages over a family of sparse sequences, J. Anal. Math. 138 (2019), no. 1, 1–21. MR 3996030, DOI 10.1007/s11854-019-0020-z
Richard A. Hunt, On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967) Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235–255. MR 0238019
Isroil A. Ikromov, Michael Kempe, and Detlef Müller, Estimates for maximal functions associated with hypersurfaces in $\Bbb R^3$ and related problems of harmonic analysis, Acta Math. 204 (2010), no. 2, 151–271. MR 2653054, DOI 10.1007/s11511-010-0047-6
Alexandru D. Ionescu, An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators, Ann. of Math. (2) 152 (2000), no. 1, 259–275. MR 1792296, DOI 10.2307/2661383
Alexandru D. Ionescu, An endpoint estimate for the discrete spherical maximal function, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1411–1417. MR 2053347, DOI 10.1090/S0002-9939-03-07207-1
Alexandru D. Ionescu, Rearrangement inequalities on semisimple Lie groups, Math. Ann. 332 (2005), no. 4, 739–758. MR 2179774, DOI 10.1007/s00208-005-0650-6
Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger, Averages along polynomial sequences in discrete nilpotent Lie groups: singular Radon transforms, Advances in analysis: the legacy of Elias M. Stein, Princeton Math. Ser., vol. 50, Princeton Univ. Press, Princeton, NJ, 2014, pp. 146–188. MR 3329850
Alexandru D. Ionescu and Stephen Wainger, $L^p$ boundedness of discrete singular Radon transforms, J. Amer. Math. Soc. 19 (2006), no. 2, 357–383. MR 2188130, DOI 10.1090/S0894-0347-05-00508-4
B. Jessen, J. Marcinkiewicz, and A. Zygmund, Note on the differentiability of multiple integrals, Fund. Math. 25 (1935), 217-234.
Roger L. Jones, Andreas Seeger, and James Wright, Strong variational and jump inequalities in harmonic analysis, Trans. Amer. Math. Soc. 360 (2008), no. 12, 6711–6742. MR 2434308, DOI 10.1090/S0002-9947-08-04538-8
V. N. Karpushkin, A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables, J. Soviet Math. 35 (1986) 2809-2826.
Robert Kesler, Michael T. Lacey, and Darío Mena, Sparse bounds for the discrete spherical maximal functions, Pure Appl. Anal. 2 (2020), no. 1, 75–92. MR 4041278, DOI 10.2140/paa.2020.2.75
Kenneth D. Koenig, On maximal Sobolev and Hölder estimates for the tangential Cauchy-Riemann operator and boundary Laplacian, Amer. J. Math. 124 (2002), no. 1, 129–197. MR 1879002
A. Kolmogorov, Une série de Fourier-Lebesgue divergente presque partout, Fund. Math. 4 (1923), 324-328.
T. W. Körner, Fourier analysis, Cambridge University Press, Cambridge, 1988. MR 924154, DOI 10.1017/CBO9781107049949
Michael Lacey and Christoph Thiele, A proof of boundedness of the Carleson operator, Math. Res. Lett. 7 (2000), no. 4, 361–370. MR 1783613, DOI 10.4310/MRL.2000.v7.n4.a1
Victor Lie, The (weak-$L^2$) boundedness of the quadratic Carleson operator, Geom. Funct. Anal. 19 (2009), no. 2, 457–497. MR 2545246, DOI 10.1007/s00039-009-0010-x
V. Lie, A note on the polynomial Carleson operator in higher dimensions, arXiv:1712.03092 (2017).
N. N. Luzin, Integral i trigonometričeskiĭ ryad, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1951 (Russian). Editing and commentary by N. K. Bari and D. E. Men′šov. MR 0048364
Matei Machedon, Estimates for the parametrix of the Kohn Laplacian on certain domains, Invent. Math. 91 (1988), no. 2, 339–364. MR 922804, DOI 10.1007/BF01389371
Akos Magyar, $L^p$-bounds for spherical maximal operators on $\mathbf Z^n$, Rev. Mat. Iberoamericana 13 (1997), no. 2, 307–317. MR 1617657, DOI 10.4171/RMI/222
Giancarlo Mauceri, Zonal multipliers on the Heisenberg group, Pacific J. Math. 95 (1981), no. 1, 143–159. MR 631666
Jeffery D. McNeal, Boundary behavior of the Bergman kernel function in $\textbf {C}^2$, Duke Math. J. 58 (1989), no. 2, 499–512. MR 1016431, DOI 10.1215/S0012-7094-89-05822-5
Mariusz Mirek, Square function estimates for discrete Radon transforms, Anal. PDE 11 (2018), no. 3, 583–608. MR 3738256, DOI 10.2140/apde.2018.11.583
Detlef Müller, A geometric bound for maximal functions associated to convex bodies, Pacific J. Math. 142 (1990), no. 2, 297–312. MR 1042048
Alexander Nagel, Néstor Rivière, and Stephen Wainger, On Hilbert transforms along curves, Bull. Amer. Math. Soc. 80 (1974), 106–108. MR 450899, DOI 10.1090/S0002-9904-1974-13374-4
Alexander Nagel, Nestor Riviere, and Stephen Wainger, A maximal function associated to the curve $(t, t^{2})$, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 5, 1416–1417. MR 399389, DOI 10.1073/pnas.73.5.1416
Alexander Nagel, Néstor M. Rivière, and Stephen Wainger, On Hilbert transforms along curves. II, Amer. J. Math. 98 (1976), no. 2, 395–403. MR 450900, DOI 10.2307/2373893
Alexander Nagel and Stephen Wainger, $L^{2}$ boundedness of Hilbert transforms along surfaces and convolution operators homogeneous with respect to a multiple parameter group, Amer. J. Math. 99 (1977), no. 4, 761–785. MR 450901, DOI 10.2307/2373864
F. Nazarov, S. Treil, and A. Volberg, The $Tb$-theorem on non-homogeneous spaces, Acta Math. 190 (2003), no. 2, 151–239. MR 1998349, DOI 10.1007/BF02392690
Daniel M. Oberlin, Two discrete fractional integrals, Math. Res. Lett. 8 (2001), no. 1-2, 1–6. MR 1825254, DOI 10.4310/MRL.2001.v8.n1.a1
D. H. Phong, On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), no. 4, 1554–1558. MR 526179, DOI 10.1073/pnas.76.4.1554
Lillian B. Pierce, On discrete fractional integral operators and mean values of Weyl sums, Bull. Lond. Math. Soc. 43 (2011), no. 3, 597–612. MR 2820148, DOI 10.1112/blms/bdq127
Lillian B. Pierce, Discrete fractional Radon transforms and quadratic forms, Duke Math. J. 161 (2012), no. 1, 69–106. MR 2872554, DOI 10.1215/00127094-1507288
Lillian B. Pierce and Po-Lam Yung, A polynomial Carleson operator along the paraboloid, Rev. Mat. Iberoam. 35 (2019), no. 2, 339–422. MR 3945729, DOI 10.4171/rmi/1057
R. Michael Range, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, vol. 108, Springer-Verlag, New York, 1986. MR 847923, DOI 10.1007/978-1-4757-1918-5
Vyacheslav S. Rychkov, Sharp $L^2$ bounds for oscillatory integral operators with $C^\infty$ phases, Math. Z. 236 (2001), no. 3, 461–489. MR 1821301, DOI 10.1007/PL00004838
Andreas Seeger, Radon transforms and finite type conditions, J. Amer. Math. Soc. 11 (1998), no. 4, 869–897. MR 1623430, DOI 10.1090/S0894-0347-98-00280-X
Per Sjölin, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat. 9 (1971), 65–90. MR 336222, DOI 10.1007/BF02383638
Christopher D. Sogge, Concerning the $L^p$ norm of spectral clusters for second-order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), no. 1, 123–138. MR 930395, DOI 10.1016/0022-1236(88)90081-X
Christopher D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), no. 2, 349–376. MR 1098614, DOI 10.1007/BF01245080
Brian Street, Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius, Rev. Mat. Iberoam. 27 (2011), no. 2, 645–732. MR 2848534, DOI 10.4171/RMI/650
Brian Street, Multi-parameter singular Radon transforms I: The $L^2$ theory, J. Anal. Math. 116 (2012), 83–162. MR 2892618, DOI 10.1007/s11854-012-0004-8
Robert S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), no. 3, 705–714. MR 512086
Jan-Olov Strömberg, Weak type $L^{1}$ estimates for maximal functions on noncompact symmetric spaces, Ann. of Math. (2) 114 (1981), no. 1, 115–126. MR 625348, DOI 10.2307/1971380
Terence Tao, The Bochner-Riesz conjecture implies the restriction conjecture, Duke Math. J. 96 (1999), no. 2, 363–375. MR 1666558, DOI 10.1215/S0012-7094-99-09610-2
Terence Tao, Some recent progress on the restriction conjecture, Fourier analysis and convexity, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2004, pp. 217–243. MR 2087245, DOI 10.1198/106186003321335099
Terence Tao and James Wright, $L^p$ improving bounds for averages along curves, J. Amer. Math. Soc. 16 (2003), no. 3, 605–638. MR 1969206, DOI 10.1090/S0894-0347-03-00420-X
Xavier Tolsa, Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory, Progress in Mathematics, vol. 307, Birkhäuser/Springer, Cham, 2014. MR 3154530, DOI 10.1007/978-3-319-00596-6
Peter A. Tomas, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477–478. MR 358216, DOI 10.1090/S0002-9904-1975-13790-6
Peter A. Tomas, Restriction theorems for the Fourier transform, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 111–114. MR 545245
A. N. Varčenko, Newton polyhedra and estimates of oscillatory integrals, Funkcional. Anal. i Priložen. 10 (1976), no. 3, 13–38 (Russian). MR 0422257
P. Zorin-Kranich, Maximal polynomial modulations of singular integrals, arXiv:1711. 03524 (2017).
A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
A. Zygmund, On Fourier coefficients and transforms of functions of two variables, Studia Math. 50 (1974), 189–201. MR 387950, DOI 10.4064/sm-50-2-189-201