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July, 2008 On the uniqueness of the one-sided maximal functions of Borel measures
Lasha EPHREMIDZE, Nobuhiko FUJII
J. Math. Soc. Japan 60(3): 695-717 (July, 2008). DOI: 10.2969/jmsj/06030695

Abstract

We prove that if ν and μ are arbitrary (signed) Borel measures (on the unit circle) such that M + ν(x)= M + μ(x) for each x , where M + is the one-sided maximal operator (without modulus in the definition), then ν=μ . The proof is constructive and it shows how ν can be recovered from M + ν in the unique way.

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Lasha EPHREMIDZE. Nobuhiko FUJII. "On the uniqueness of the one-sided maximal functions of Borel measures." J. Math. Soc. Japan 60 (3) 695 - 717, July, 2008. https://doi.org/10.2969/jmsj/06030695

Information

Published: July, 2008
First available in Project Euclid: 4 August 2008

zbMATH: 1268.42035
MathSciNet: MR2440410
Digital Object Identifier: 10.2969/jmsj/06030695

Subjects:
Primary: 42B25
Secondary: 28A25

Keywords: Borel measures , maximal functions , Uniqueness theorem

Rights: Copyright © 2008 Mathematical Society of Japan

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Vol.60 • No. 3 • July, 2008
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