Endpoint estimates for the circular maximal function

Author:
Sanghyuk Lee

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1433-1442

MSC (2000):
Primary 42B25; Secondary 35L05

Published electronically:
September 19, 2002

MathSciNet review:
1949873

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of endpoint estimates for the circular maximal function defined by

where is the normalized surface area measure on . Let be the closed triangle with vertices . We prove that for , there is a constant such that Furthermore, .

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Additional Information

**Sanghyuk Lee**

Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea

Email:
huk@euclid.postech.ac.kr

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06781-3

Keywords:
Circular maximal function,
endpoint estimates

Received by editor(s):
June 12, 2001

Received by editor(s) in revised form:
December 7, 2001

Published electronically:
September 19, 2002

Additional Notes:
The author was partially supported by the BK21 Project (PI: Jong-Guk Bak).

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2002
American Mathematical Society