Problems in harmonic analysis related to curvature

Stein, Elias M.; Wainger, Stephen

doi:10.1090/S0002-9904-1978-14554-6

Problems in harmonic analysis related to curvature
HTML articles powered by AMS MathViewer

by Elias M. Stein and Stephen Wainger PDF

Bull. Amer. Math. Soc. 84 (1978), 1239-1295

References

D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249–304. MR 440695, DOI 10.1007/BF02394573
A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, Advances in Math. 16 (1975), 1–64. MR 417687, DOI 10.1016/0001-8708(75)90099-7
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
A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289–309. MR 84633, DOI 10.2307/2372517
J. L. Clerc and E. M. Stein, $L^{p}$-multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911–3912. MR 367561, DOI 10.1073/pnas.71.10.3911
R. R. Coifman, Distribution function inequalities for singular integrals, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 2838–2839. MR 303226, DOI 10.1073/pnas.69.10.2838
A. Cordoba and R. Fefferman, A geometric proof of the strong maximal theorem, Ann. of Math. (2) 102 (1975), no. 1, 95–100. MR 379785, DOI 10.2307/1970976
A. Córdoba and R. Fefferman, On differentiation of integrals, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 6, 2211–2213. MR 476977, DOI 10.1073/pnas.74.6.2211
Eugene B. Fabes, Singular integrals and partial differential equations of parabolic type, Studia Math. 28 (1966/67), 81–131. MR 213744, DOI 10.4064/sm-28-1-81-131
Eugene B. Fabes, Singular integrals and partial differential equations of parabolic type, Studia Math. 28 (1966/67), 81–131. MR 213744, DOI 10.4064/sm-28-1-81-131
E. B. Fabes and N. M. Rivière, Symbolic calculus of kernels with mixed homogeneity, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 106–127. MR 0236773
Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36. MR 257819, DOI 10.1007/BF02394567
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403
Miguel de Guzmán, Differentiation of integrals in $R^{n}$, Lecture Notes in Mathematics, Vol. 481, Springer-Verlag, Berlin-New York, 1975. With appendices by Antonio Córdoba, and Robert Fefferman, and two by Roberto Moriyón. MR 0457661, DOI 10.1007/BFb0081986
Edmund Hlawka, Über Integrale auf konvexen Körpern. I, Monatsh. Math. 54 (1950), 1–36 (German). MR 37003, DOI 10.1007/BF01304101
G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), no. 1, 81–116. MR 1555303, DOI 10.1007/BF02547518
C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2) 75 (1962), 81–92. MR 142978, DOI 10.2307/1970421
C. S. Herz, On the number of lattice points in a convex set, Amer. J. Math. 84 (1962), 126–133. MR 139583, DOI 10.2307/2372808
Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
B. Frank Jones Jr., A class of singular integrals, Amer. J. Math. 86 (1964), 441–462. MR 161099, DOI 10.2307/2373175
A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
Adam Koranyi, Harmonic functions on symmetric spaces, Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), Pure and Appl. Math., Vol. 8, Dekker, New York, 1972, pp. 379–412. MR 0407541
Walter Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766–770. MR 155146, DOI 10.1090/S0002-9904-1963-11025-3
S. G. Mihlin, Singular integral equations, Amer. Math. Soc. Translation 1950 (1950), no. 24, 116. MR 0036434
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, 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 and Stephen Wainger, Hilbert transforms associated with plane curves, Trans. Amer. Math. Soc. 223 (1976), 235–252. MR 423010, DOI 10.1090/S0002-9947-1976-0423010-8
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
Burton Randol, A lattice-point problem, Trans. Amer. Math. Soc. 121 (1966), 257–268. MR 201407, DOI 10.1090/S0002-9947-1966-0201407-2
Burton Randol, The asymptotic behavior of a Fourier transform and the localization property for eigenfunction expansions for some partial differential operators, Trans. Amer. Math. Soc. 168 (1972), 265–271. MR 296600, DOI 10.1090/S0002-9947-1972-0296600-X
N. M. Rivière, Singular integrals and multiplier operators, Ark. Mat. 9 (1971), 243–278. MR 440268, DOI 10.1007/BF02383650
Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
E. M. Stein, On limits of seqences of operators, Ann. of Math. (2) 74 (1961), 140–170. MR 125392, DOI 10.2307/1970308
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
E. M. Stein, Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 173–189. MR 0578903
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
Elias M. Stein and Stephen Wainger, The estimation of an integral arising in multiplier transformations, Studia Math. 35 (1970), 101–104. MR 265995, DOI 10.4064/sm-35-1-101-104
E. M. Stein and S. Wainger, Maximal functions associated to smooth curves, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 12, 4295–4296. MR 415199, DOI 10.1073/pnas.73.12.4295
Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Jan-Olov Strömberg, Weak estimates on maximal functions with rectangles in certain directions, Ark. Mat. 15 (1977), no. 2, 229–240. MR 487260, DOI 10.1007/BF02386043
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
François Trèves, Basic linear partial differential equations, Pure and Applied Mathematics, Vol. 62, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0447753
Norbert Wiener, The ergodic theorem, Duke Math. J. 5 (1939), no. 1, 1–18. MR 1546100, DOI 10.1215/S0012-7094-39-00501-6
Felipe Zo, A note on approximation of the identity, Studia Math. 55 (1976), no. 2, 111–122. MR 423013, DOI 10.4064/sm-55-2-111-122
A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
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