Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Hilbert transforms and maximal functions associated to flat curves on the Heisenberg group


Authors: Anthony Carbery, Stephen Wainger and James Wright
Journal: J. Amer. Math. Soc. 8 (1995), 141-179
MSC: Primary 43A80; Secondary 22E20, 42B20, 42B25
DOI: https://doi.org/10.1090/S0894-0347-1995-1273412-0
MathSciNet review: 1273412
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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, $ {L^p}$ 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.
  • [C2] -, Hilbert transforms along curves, I. Nilpotent groups, Ann. of Math. (2) 122 (1985), 575-596. MR 819558 (87f:42039a)
  • [CNSW] M. Christ, A. Nagel, E. Stein, and S. Wainger, Singular and maximal Radon transforms, Ann. of Math. Stud., Princeton Univ. Press, Princeton, NJ (to appear).
  • [CW] R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Lectures Notes in Math., vol. 242, Springer-Verlag, Berlin and New York, 1971. MR 0499948 (58:17690)
  • [NSW] 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)
  • [NSW1] 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)
  • [S] E. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
  • [SS] C. Sogge and E. Stein, Averages of functions over hypersurfaces in $ {\mathbb{R}^n}$, Invent. Math. 82 (1985), 543-556. MR 811550 (87d:42030)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 43A80, 22E20, 42B20, 42B25

Retrieve articles in all journals with MSC: 43A80, 22E20, 42B20, 42B25


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1995-1273412-0
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society