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Hilbert transforms and maximal functions associated to flat curves on the Heisenberg group
Author(s):
Anthony
Carbery;
Stephen
Wainger;
James
Wright
Journal:
J. Amer. Math. Soc.
8
(1995),
141-179.
MSC:
Primary 43A80;
Secondary 22E20, 42B20, 42B25
MathSciNet review:
1273412
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Additional information
References:
-
- [CVWWA]
- A. Carbery, J. Vance, S. Wainger, and D. Watson, The Hilbert transform and maximal function along flat curves, dilations and differential equations, Amer. J. Math. (to appear). MR 1296728 (95m:42022)
- [CVWWW]
- A. Carbery, J. Vance, S. Wainger, D. Watson, and J. Wright,
estimates for operators associated to flat curves without the Fourier transform, Pacific J. Math (to appear). MR 1328328 (96b:42018) - [CVWW]
- A. Carbery, J. Vance, S. Wainger, and J. Wright, A variant of the notion of a space of homogeneous type (to appear).
- [CZ]
- A. Carbery and S. Ziesler, Hilbert transforms and maximal functions along rough flat curves (to appear). MR 1286480 (95h:42016)
- [C1]
- M. Christ, Hilbert transforms along curves, III. Rotational curvature, preprint, 1985.
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- -, Hilbert transforms along curves, I. Nilpotent groups, Ann. of Math. (2) 122 (1985), 575-596. MR 819558 (87f:42039a)
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- A. Nagel, E. Stein, and S. Wainger, Hilbert transforms and maximal functions related to variable curves, Proc. Sympos. Pure Math., vol. 35, Part 2, Amer. Math. Soc., Providence, RI, 1979, pp. 95-98. MR 545242 (81a:42027)
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- A. Nagel, E. Stein, and S. Wainger, Differentiation in lacunary directions, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 1060-1062. MR 0466470 (57:6349)
- [RS]
- F. Ricci and E. Stein, Harmonic analysis on nilpotent groups and singular integrals, III. Kernels supported on submanifolds, J. Funct. Anal. 78 (1988), 56-84. MR 937632 (89g:42030)
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- E. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
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- C. Sogge and E. Stein, Averages of functions over hypersurfaces in
, Invent. Math. 82 (1985), 543-556. MR 811550 (87d:42030)
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Additional Information:
DOI:
10.1090/S0894-0347-1995-1273412-0
PII:
S0894-0347-1995-1273412-0
Copyright of article:
Copyright
1995,
American Mathematical Society
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