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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1936-881X(e) ISSN 0002-9904(p)
     

Problems in harmonic analysis related to curvature

Author(s): Elias M. Stein; Stephen Wainger
Journal: Bull. Amer. Math. Soc. 84 (1978), 1239-1295.
MSC (1970): Primary 42A68, 28A15, 44A25
MathSciNet review: 508453
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References:

D. Burkholder and R. Gundy [1970], Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124, 249-304. MR 440695

H. Buseman and W. Feller [1934], Differentiation der L-integrale, Fund. Math. 22, 226-256.

A. P. Calderón and A. Torchinsky [1975], Parabolic maximal functions associated with a distribution, Advances in Math. 16, 1-64. MR 417687

A. P. Calderón and A. Zygmund [1952], On the existence of certain singular integrals, Acta Math. 88, 85-139. MR 52553

A. P. Calderón and A. Zygmund, [1956], On singular integrals, Amer. J. Math. 18, 289-309. MR 84633

J. L. Clerc and E. M. Stein [1974], L, Proc. Nat Acad. Sci. U.S.A. 71, 3911-3912. MR 367561

R. Coifman [1972], Distribution function inequalities for singular integrals, Proc. Nat Acad. Sci. U.S.A. 69, 2838-2839. MR 303226

A. Cordoba and R. Fefferman [1975], A geometric proof of the strong maximal theorem, Ann. of Math. (2) 102, 95-100. MR 379785

A. Cordoba and R. Fefferman, [1977], On differentiation of integrals, Proc. Nat. Acad. Sci. U.S.A. 74, 2211-2213. MR 476977

A. Erdélyi [1953], Higher transcendental functions, vol. 2, McGraw-Hill, New York.

E. B. Fabes [1966], Singular integrals and partial differential equations of parabolic type, Studia Math. 28 81-131. MR 213744

E. B. Fabes and N. M. Rivière [1966], Singular integrals with mixed homogeneity, Studia Math. 27, 19-38. MR 213744

E. B. Fabes and N. M. Rivière, [1967], Symbolic calculus of kernels with mixed homogeneity, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R.I. MR 236773

C. Fefferman [1970], Inequalities for strongly singular convolution operators, Acta Math. 124, 9-36. MR 257819

C. Fefferman and E. M. Stein [1972], H, Acta Math. 229, 137-193. MR 447953

G. B. Folland and E. M. Stein [1974], Estimates for the $\bar \partial \sbb$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27, 429-522. MR 367477

M. de Guzman [1975], Differentiation of integrals in R, Springer-Verlag, Berlin and New York. MR 457661

E. Hlawka [1950], Über Integrale auf konvexen Körpern. I, Monatsh. Math. 54, 1-36. MR 37003

G. H. Hardy [1949], Divergent series, Clarendon Press, Oxford. MR 30620

G. H. Hardy and J. E. Littlewood [1930], A maximal theorem with function-theoretic applications, Acta Math. 54, 81-116. MR 1555303

C. S. Herz [1962a], Fourier transforms related to convex sets, Ann. of Math. (2) 75, 81-92. MR 142978

C. S. Herz, [1962b], On the number of lattice points in a convex set, Amer. J. Math. 84, 126-133. MR 139583

L. Hörmander [1967], Hypoelliptic second order differential equations, Acta Math. 119, 147-171. MR 222474

B. F. Jones [1964], A class of singular integrals, Amer. J. Math. 86, 441-462. MR 161099

S. Kaczmarz and H. Steinhaus [1951], Theorie der Orthogonalreihen, Chelsea, New York.

A. W. Knapp and E. M. Stein [1971], Intertwining operators for semi-simple Lie groups, Ann. of Math. (2) 93, 489-578. MR 460543

A. Koranyi [1972], Harmonic functions on symmetric spaces, Symmetric Spaces, Boothby and Weiss, eds., Marcel Dekker, New York, pp. 379-412. MR 407541

J. E. Littlewood and R.E.A.C Paley [1931], [1936], [1937], Theorems on Fourier Series and Power Series, (I), J. London Math. Soc. 6, 230-233; (II) Proc. London Math. Soc. 42, 52-89; (III) ibid. 43, 105-126.

W. Littman [1963], Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69, 766-770. MR 155146

J. Marcinkiewicz and A. Zygmund [1939], On the summability of double Fourier series, Fund. Math. 32, 112-132.

S. Mihlin [1950], Singular integral equations, Amer. Math. Soc. Transl. (1) 10 (1962), 84-198. MR 36434

A. Nagel, N. M. Rivière, and S. Wainger [1974], On Hilbert transforms along curves, Bull. Amer. Math. Soc. 80, 106-108. MR 450899

A. Nagel, N. M. Rivière, and S. Wainger, [1976a], On Hilbert transforms along curves, II, Amer. J. Math. 98, 395-403. MR 450900

A. Nagel, N. M. Rivière, and S. Wainger, [1976b], A maximal function associated to the curve (t, t, Proc. Nat. Acad. Sci. U.S.A. 73, 1416-1417.

A. Nagel and S. Wainger [1976], Hilbert transforms associated with plane curves, Trans. Amer. Math. Soc. 223, 235-252. MR 423010

A. Nagel and S. Wainger, [1977], L, Amer. J. Math. 99, 761-785. MR 450901

B. Randol [1966], A lattice-point problem, Trans. Amer. Math. Soc. 121, 257-268. MR 201407

B. Randol, [1972], The asymptotic behavior of a Fourier transform and the localization property for eigenfunction expansions, Trans. Amer. Math. Soc. 168, 265-271. MR 296600

N. M. Rivière [1971], Singular integrals and multiplier operators, Ark. Mat. 9, 243-278. MR 440268

L. Rothschild and E. Stein [1976], Hypoelliptic differential operators and nilpotent groups, Acta Math. 137, 247-320. MR 436223

E. M. Stein [1961], On limits of sequences of operators, Ann. of Math. (2) 74, 140-170. MR 125392

E. M. Stein, [1970a], Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N J. MR 290095

E. M. Stein, [1970b], Topics in harmonic analysis related to the Littlewood-Paley theory, Princeton Univ. Press, Princeton, N. J. MR 252961

E. M. Stein, [1971], Some problems in harmonic analysis suggested by symmetric spaces and semi-simple Lie groups, Actes, Internat. Congr. Math., 1, pp. 173-189. MR 578903

E. M. Stein, [1976a], Maximal functions: Spherical means, Proc. Nat. Acad. Sci. U.SA. 73, 2174-2175. MR 420116

E. M. Stein, [1976b], Maximal functions: homogeneous curves, Proc. Nat. Acad. Sci. U.SA. 73, 2176-2177. MR 420117

E. M. Stein, [1976c], Maximal functions: Poisson integrals on symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 73, 2547-2549. MR 420118

E. M. Stein and S. Wainger [1970], The estimation of an integral arising in multiplier transformations, Studia Math. 35, 101-104. MR 265995

E. M. Stein and S. Wainger, [1976], Maximal functions associated to smooth curves, Proc. Nat. Acad. Sci. U.S.A. 73, pp. 4295-4296. MR 415199

E. M. Stein and G. Weiss [1971], Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N.J. MR 304972

J. O. Strömberg [1976], (a) Weak estimates for maximal functions with rectangles in certain directions, Institut Mittag-Leffler, report #10, Ark. Mat. 15 (1977), 229-240. MR 487260

E. C. Titchmarsh [1937], Introduction to the theory of the Fourier integral, Oxford Univ. Press, London.

P. Tomas [1975], A restriction theorem for the Fourier transform, Bull. Amcr. Math. Soc. 81, 477-478. MR 358216

F. Treves [1975], Basic linear partial differential equations, Academic Press, New York. MR 447753

N. Wiener [1939], The ergodic theorem, Duke Math. J. 5, 1-18. MR 1546100

K. Yosida [1965], Functional analysis, Springer-Verlag, Berlin and New York.

F. Zo [1977], A note on approximation of the identity, Studia Math. 55, 111-122. MR 423013

F. Zo, [1975], Pointwise convergence for integrable functions, Ph. D. Dissertation, Univ. of Minnesota, Minneapolis, Minn.

A. Zygmund [1959], Trigonometric series, vols. 1 and 2, Cambridge Univ. Press, London. MR 107776

A. Zygmund, [1974], On Fourier coefficients and transforms of two variables, Studia Math. 50, 189-201. MR 387950


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Additional Information:

DOI: 10.1090/S0002-9904-1978-14554-6
PII: S 0002-9904(1978)14554-6


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