The strong maximal function on a nilpotent group

Christ, Michael

doi:10.1090/S0002-9947-1992-1104197-X

The strong maximal function on a nilpotent group
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by Michael Christ PDF

Trans. Amer. Math. Soc. 331 (1992), 1-13 Request permission

Abstract:

An analogue of the strong maximal function of Jessen, Marcinkiewicz, and Zygmund is shown to be bounded on ${L^p}$, for all $p > 1$, on a nilpotent Lie group.

References

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
Hasse Carlsson, Peter Sjögren, and Jan-Olov Strömberg, Multiparameter maximal functions along dilation-invariant hypersurfaces, Trans. Amer. Math. Soc. 292 (1985), no. 1, 335–343. MR 805966, DOI 10.1090/S0002-9947-1985-0805966-X
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

Hilbert transforms along curves

Rotational curvature

Note on the differentiability of multiple integrals

25

D. H. Phong and E. M. Stein, Singular integrals related to the Radon transform and boundary value problems, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), no. 24, , Phys. Sci., 7697–7701. MR 728667, DOI 10.1073/pnas.80.24.7697

Hilbert integrals, singular integrals and Radon transforms

157

Hasse Carlsson, Peter Sjögren, and Jan-Olov Strömberg, Multiparameter maximal functions along dilation-invariant hypersurfaces, Trans. Amer. Math. Soc. 292 (1985), no. 1, 335–343. MR 805966, DOI 10.1090/S0002-9947-1985-0805966-X

Two-parameter maximal functions on the Heisenberg group

F. Ricci and E. M. Stein, Oscillatory singular integrals and harmonic analysis on nilpotent groups, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 1, 1–3. MR 822187, DOI 10.1073/pnas.83.1.1
Fulvio Ricci and Elias M. Stein, Harmonic analysis on nilpotent groups and singular integrals. II. Singular kernels supported on submanifolds, J. Funct. Anal. 78 (1988), no. 1, 56–84. MR 937632, DOI 10.1016/0022-1236(88)90132-2
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, Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals, Invent. Math. 74 (1983), no. 1, 63–83. MR 722726, DOI 10.1007/BF01388531
Elias M. Stein and Stephen Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295. MR 508453, DOI 10.1090/S0002-9904-1978-14554-6