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December 2015 John-Nirenberg Inequalities with Variable Exponents on Probability Spaces
Zhiwei HAO, Yong JIAO, Lian WU
Tokyo J. Math. 38(2): 353-367 (December 2015). DOI: 10.3836/tjm/1452806045

Abstract

In this paper we study the John-Nirenberg inequalities with variable exponents on a probability space. Let $Y$ be a rearrangement invariant Banach function space defined on $(\Omega,\mathcal{F},P)$ and a measurable function $p(\cdot): \Omega\rightarrow \mathbf{R}^+$ be a variable exponent. We prove that if the stochastic basis is regular, then $$BMO_{\phi,Y}=BMO_{\phi,p(\cdot)}\,,\quad \forall 1\leq p(\cdot)<\infty\,,$$ where $\phi(r)=1/r\Phi^{-1}(1/r)$ and $\Phi$ is a concave function with proper condition.

Citation

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Zhiwei HAO. Yong JIAO. Lian WU. "John-Nirenberg Inequalities with Variable Exponents on Probability Spaces." Tokyo J. Math. 38 (2) 353 - 367, December 2015. https://doi.org/10.3836/tjm/1452806045

Information

Published: December 2015
First available in Project Euclid: 14 January 2016

zbMATH: 1364.60053
MathSciNet: MR3448862
Digital Object Identifier: 10.3836/tjm/1452806045

Subjects:
Primary: 60G42
Secondary: 60G46

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

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Vol.38 • No. 2 • December 2015
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