Maximal theorems for the directional Hilbert transform on the plane

Authors:
Michael T. Lacey and Xiaochun Li

Journal:
Trans. Amer. Math. Soc. **358** (2006), 4099-4117

MSC (2000):
Primary 42B20, 42B25; Secondary 42B05

DOI:
https://doi.org/10.1090/S0002-9947-06-03869-4

Published electronically:
March 24, 2006

MathSciNet review:
2219012

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a Schwartz function on the plane and a non-zero define the Hilbert transform of in the direction to be

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Additional Information

**Michael T. Lacey**

Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332

Email:
lacey@math.gatech.edu

**Xiaochun Li**

Affiliation:
Department of Mathematics, University of California–Los Angeles, Los Angeles, California 90055-1555

Address at time of publication:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540

Email:
xcli@math.ucla.edu

DOI:
https://doi.org/10.1090/S0002-9947-06-03869-4

Keywords:
Hilbert transform,
Fourier series,
maximal function,
pointwise convergence

Received by editor(s):
October 23, 2003

Received by editor(s) in revised form:
August 24, 2004

Published electronically:
March 24, 2006

Additional Notes:
The research of both authors was supported in part by NSF grants; the first author was also supported by the Guggenheim Foundation. Some of this research was completed during research stays by the first author at the Universite d’Paris-Sud, Orsay, and the Erwin Schrödinger Institute of Vienna Austria. The generosity of both is gratefully acknowledged.

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.