Tokyo Journal of Mathematics

John-Nirenberg Inequalities with Variable Exponents on Probability Spaces

Zhiwei HAO, Yong JIAO, and Lian WU

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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.

Article information

Source
Tokyo J. Math., Volume 38, Number 2 (2015), 353-367.

Dates
First available in Project Euclid: 14 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1452806045

Digital Object Identifier
doi:10.3836/tjm/1452806045

Mathematical Reviews number (MathSciNet)
MR3448862

Zentralblatt MATH identifier
1364.60053

Subjects
Primary: 60G42: Martingales with discrete parameter
Secondary: 60G46: Martingales and classical analysis

Citation

WU, Lian; HAO, Zhiwei; JIAO, Yong. John-Nirenberg Inequalities with Variable Exponents on Probability Spaces. Tokyo J. Math. 38 (2015), no. 2, 353--367. doi:10.3836/tjm/1452806045. https://projecteuclid.org/euclid.tjm/1452806045


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