Bulletin of the American Mathematical Society

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Book Information:

Authors: C. Muscalu and W. Schlag
Title: Classical and multilinear harmonic analysis, Volume 1
Additional book information: Cambridge Studies in Advanced Mathematics, 137, Cambridge University Press, Cambridge, 2013, xviii+370 pp., ISBN 978-0-521-88245-3

Authors: C. Muscalu and W. Schlag
Title: Classical and multilinear harmonic analysis, Volume 2
Additional book information: Cambridge Studies in Advanced Mathematics, 138, Cambridge University Press, Cambridge, 2013, xvi+324 pp., ISBN 978-1-107-03182-1

Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Ph. Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on ${\Bbb R}^n$, Ann. of Math. (2) 156 (2002), no. 2, 633–654. MR 1933726, DOI 10.2307/3597201

Jonathan Bennett, Anthony Carbery, and Terence Tao, On the multilinear restriction and Kakeya conjectures, Acta Math. 196 (2006), no. 2, 261–302. MR 2275834, DOI 10.1007/s11511-006-0006-4

J. Bourgain, On the dimension of Kakeya sets and related maximal inequalities, Geom. Funct. Anal. 9 (1999), no. 2, 256–282. MR 1692486, DOI 10.1007/s000390050087

J. Bourgain, N. Katz, and T. Tao, A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14 (2004), no. 1, 27–57. MR 2053599, DOI 10.1007/s00039-004-0451-1

A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 52553, DOI 10.1007/BF02392130

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, 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

Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948

R. R. Coifman and Yves Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315–331. MR 380244, DOI 10.1090/S0002-9947-1975-0380244-8

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

Yves Meyer and R. R. Coifman, Ondelettes et opérateurs. III, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1991 (French). Opérateurs multilinéaires. [Multilinear operators]. MR 1160989

Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911, DOI 10.2307/2006946

G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56 (French). MR 850408, DOI 10.4171/RMI/17

Zeev Dvir, On the size of Kakeya sets in finite fields, J. Amer. Math. Soc. 22 (2009), no. 4, 1093–1097. MR 2525780, DOI 10.1090/S0894-0347-08-00607-3

Charles Fefferman, Pointwise convergence of Fourier series, Ann. of Math. (2) 98 (1973), 551–571. MR 340926, DOI 10.2307/1970917

Loukas Grafakos and Rodolfo H. Torres, Multilinear Calderón-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124–164. MR 1880324, DOI 10.1006/aima.2001.2028

Larry Guth, The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263–286. MR 2746348, DOI 10.1007/s11511-010-0055-6

Tuomas P. Hytönen, The sharp weighted bound for general Calderón-Zygmund operators, Ann. of Math. (2) 175 (2012), no. 3, 1473–1506. MR 2912709, DOI 10.4007/annals.2012.175.3.9

Carlos E. Kenig and Elias M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), no. 1, 1–15. MR 1682725, DOI 10.4310/MRL.1999.v6.n1.a1

Michael Lacey and Christoph Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2<p<\infty$, Ann. of Math. (2) 146 (1997), no. 3, 693–724. MR 1491450, DOI 10.2307/2952458

Michael Lacey and Christoph Thiele, On Calderón’s conjecture, Ann. of Math. (2) 149 (1999), no. 2, 475–496. MR 1689336, DOI 10.2307/120971

Alan McIntosh and Yves Meyer, Algèbres d’opérateurs définis par des intégrales singulières, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 8, 395–397 (French, with English summary). MR 808636

Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6

Camil Muscalu, Terence Tao, and Christoph Thiele, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. 15 (2002), no. 2, 469–496. MR 1887641, DOI 10.1090/S0894-0347-01-00379-4

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

Stefanie Petermichl and Alexander Volberg, Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular, Duke Math. J. 112 (2002), no. 2, 281–305. MR 1894362, DOI 10.1215/S0012-9074-02-11223-X

T. Tao, A sharp bilinear restrictions estimate for paraboloids, Geom. Funct. Anal. 13 (2003), no. 6, 1359–1384. MR 2033842, DOI 10.1007/s00039-003-0449-0

Xavier Tolsa, Painlevé’s problem and the semiadditivity of analytic capacity, Acta Math. 190 (2003), no. 1, 105–149. MR 1982794, DOI 10.1007/BF02393237

Thomas Wolff, A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153 (2001), no. 3, 661–698. MR 1836285, DOI 10.2307/2661365

• Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Ph. Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on ${\mathbb {R}}^n$, Ann. of Math. (2) 156 (2002), no. 2, 633–654. MR 1933726 (2004c:47096c), DOI 10.2307/3597201
• Jonathan Bennett, Anthony Carbery, and Terence Tao, On the multilinear restriction and Kakeya conjectures, Acta Math. 196 (2006), no. 2, 261–302. MR 2275834 (2007h:42019), DOI 10.1007/s11511-006-0006-4
• J. Bourgain, On the dimension of Kakeya sets and related maximal inequalities, Geom. Funct. Anal. 9 (1999), no. 2, 256–282. MR 1692486 (2000b:42013), DOI 10.1007/s000390050087
• J. Bourgain, N. Katz, and T. Tao, A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14 (2004), no. 1, 27–57. MR 2053599 (2005d:11028), DOI 10.1007/s00039-004-0451-1
• A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 0052553 (14,637f)
• Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 0199631 (33 \#7774)
• 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 (92k:42020)
• Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Étude de certaines intégrales singulières, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). MR 0499948 (58 \#17690)
• R. R. Coifman and Yves Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315–331. MR 0380244 (52 \#1144)
• 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 (84m:42027), DOI 10.2307/2007065
• Yves Meyer and R. R. Coifman, Ondelettes et opérateurs. III, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1991 (French). Opérateurs multilinéaires. [Multilinear operators]. MR 1160989 (93i:42004)
• Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911 (85k:42041), DOI 10.2307/2006946
• G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56 (French). MR 850408 (88f:47024), DOI 10.4171/RMI/17
• Zeev Dvir, On the size of Kakeya sets in finite fields, J. Amer. Math. Soc. 22 (2009), no. 4, 1093–1097. MR 2525780 (2011a:52039), DOI 10.1090/S0894-0347-08-00607-3
• Charles Fefferman, Pointwise convergence of Fourier series, Ann. of Math. (2) 98 (1973), 551–571. MR 0340926 (49 \#5676)
• Loukas Grafakos and Rodolfo H. Torres, Multilinear Calderón-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124–164. MR 1880324 (2002j:42029), DOI 10.1006/aima.2001.2028
• Larry Guth, The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263–286. MR 2746348 (2012c:42027), DOI 10.1007/s11511-010-0055-6
• Tuomas P. Hytönen, The sharp weighted bound for general Calderón-Zygmund operators, Ann. of Math. (2) 175 (2012), no. 3, 1473–1506. MR 2912709, DOI 10.4007/annals.2012.175.3.9
• Carlos E. Kenig and Elias M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), no. 1, 1–15. MR 1682725 (2000k:42023a), DOI 10.4310/MRL.1999.v6.n1.a1
• Michael Lacey and Christoph Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2<p<\infty$, Ann. of Math. (2) 146 (1997), no. 3, 693–724. MR 1491450 (99b:42014), DOI 10.2307/2952458
• Michael Lacey and Christoph Thiele, On Calderón’s conjecture, Ann. of Math. (2) 149 (1999), no. 2, 475–496. MR 1689336 (2000d:42003), DOI 10.2307/120971
• Alan McIntosh and Yves Meyer, Algèbres d’opérateurs définis par des intégrales singulières, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 8, 395–397 (French, with English summary). MR 808636 (87b:47053)
• Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 0293384 (45 \#2461)
• Camil Muscalu, Terence Tao, and Christoph Thiele, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. 15 (2002), no. 2, 469–496. MR 1887641 (2003b:42017), DOI 10.1090/S0894-0347-01-00379-4
• F. Nazarov, S. Treil, and A. Volberg, The $Tb$-theorem on non-homogeneous spaces, Acta Math. 190 (2003), no. 2, 151–239. MR 1998349 (2005d:30053), DOI 10.1007/BF02392690
• Stefanie Petermichl and Alexander Volberg, Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular, Duke Math. J. 112 (2002), no. 2, 281–305. MR 1894362 (2003d:42025), DOI 10.1215/S0012-9074-02-11223-X
• T. Tao, A sharp bilinear restrictions estimate for paraboloids, Geom. Funct. Anal. 13 (2003), no. 6, 1359–1384. MR 2033842 (2004m:47111), DOI 10.1007/s00039-003-0449-0
• Xavier Tolsa, Painlevé’s problem and the semiadditivity of analytic capacity, Acta Math. 190 (2003), no. 1, 105–149. MR 1982794 (2005c:30020), DOI 10.1007/BF02393237
• Thomas Wolff, A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153 (2001), no. 3, 661–698. MR 1836285 (2002j:42019), DOI 10.2307/2661365