The Fefferman-Stein type inequality for the Kakeya maximal operator in Wolff's range

Author:
Hitoshi Tanaka

Journal:
Proc. Amer. Math. Soc. **133** (2005), 763-772

MSC (2000):
Primary 42B25

DOI:
https://doi.org/10.1090/S0002-9939-04-07623-3

Published electronically:
August 20, 2004

MathSciNet review:
2113926

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , , be the Kakeya (Nikodým) maximal operator defined as the supremum of averages over tubes of eccentricity . The (so-called) Fefferman-Stein type inequality:

is shown in the range , where and are some constants depending only on and the dimension and is a weight. The result is a sharp bound up to -factors.

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Additional Information

**Hitoshi Tanaka**

Affiliation:
Department of Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

Email:
htanaka@ms.u-tokyo.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-04-07623-3

Received by editor(s):
October 22, 2003

Published electronically:
August 20, 2004

Additional Notes:
This work was supported by the Fūjyukai Foundation.

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2004
American Mathematical Society