Lebesgue spaces with variable exponent on a probability space

Lebesgue spaces with variable exponent on a probability space

Hiroyuki Aoyama

Source: Hiroshima Math. J. Volume 39, Number 2 (2009), 207-216.

Abstract

We show that the Lebesgue space with a variable exponent $L_{p(\cdot )}$ is a rearrangement--invariant space if and only if $p$ is constant. In addition, we give a necessary and sufficient condition on a variable exponent for a martingale inequality to hold.

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Related Works:

See Correction: Erratum to ‘‘Lebesgue spaces with variable exponent on a probability space’’. Hiroshima Math. J., vol. 40, no. 2 (July, 2010), 269.

Primary Subjects: 46E30

Secondary Subjects: 60G42

Keywords: Generalized Lebesgue space; variable exponent; martingale; Doob's inequality

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1249046337
Mathematical Reviews number (MathSciNet): MR2543650
Zentralblatt MATH identifier: 1190.46026

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