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Journal of Function Spaces and Applications
Volume 5, Issue 3, Pages 319-331
http://dx.doi.org/10.1155/2007/746031

The Riesz “rising sun” lemma for arbitrary Borel measures with some applications

1A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi 0193, Georgia
2Department of Mathematics, Tokai University, Shizuoka, 424-8610, Japan
3Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Received 1 July 2006

Academic Editor: Vakhtang Kokilashvili

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak (1,1) type inequality for the corresponding Hardy-Littlewood maximal operator.