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

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

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.

Bibliographic Details
Main Authors: Lasha Ephremidze, Nobuhiko Fujii, Yutaka Terasawa
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2007/746031
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spelling doaj-c1744cd8641d4595b79374b76b04a3682020-11-24T23:45:13ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022007-01-015331933110.1155/2007/746031The Riesz “rising sun” lemma for arbitrary Borel measures with some applicationsLasha Ephremidze0Nobuhiko Fujii1Yutaka Terasawa2A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi 0193, GeorgiaDepartment of Mathematics, Tokai University, Shizuoka, 424-8610, JapanDepartment of Mathematics, Hokkaido University, Sapporo 060-0810, JapanThe 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.http://dx.doi.org/10.1155/2007/746031
collection DOAJ
language English
format Article
sources DOAJ
author Lasha Ephremidze
Nobuhiko Fujii
Yutaka Terasawa
spellingShingle Lasha Ephremidze
Nobuhiko Fujii
Yutaka Terasawa
The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
Journal of Function Spaces and Applications
author_facet Lasha Ephremidze
Nobuhiko Fujii
Yutaka Terasawa
author_sort Lasha Ephremidze
title The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
title_short The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
title_full The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
title_fullStr The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
title_full_unstemmed The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
title_sort riesz “rising sun” lemma for arbitrary borel measures with some applications
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
publishDate 2007-01-01
description 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.
url http://dx.doi.org/10.1155/2007/746031
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