On some martingale inequalities for mean oscillations in weak spaces

Masato Kikuchi

doi:10.1007/s11587-015-0224-1

On some martingale inequalities for mean oscillations in weak spaces

Masato Kikuchi^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Given a Banach function space X over a nonatomic probability space, we define, in a natural way, a quasi-Banach function space which is denoted by w-X. In this paper, we consider some inequalities in w-X involving the mean oscillation and the maximal function of a martingale. The main results give necessary and sufficient conditions for the inequalities to be valid.

Original language	English
Pages (from-to)	137-165
Number of pages	29
Journal	Ricerche di Matematica
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s11587-015-0224-1
State	Published - 2015/06/12

Keywords

Banach function space
Inequality
Martingale

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s11587-015-0224-1

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abstract = "Given a Banach function space X over a nonatomic probability space, we define, in a natural way, a quasi-Banach function space which is denoted by w-X. In this paper, we consider some inequalities in w-X involving the mean oscillation and the maximal function of a martingale. The main results give necessary and sufficient conditions for the inequalities to be valid.",

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AB - Given a Banach function space X over a nonatomic probability space, we define, in a natural way, a quasi-Banach function space which is denoted by w-X. In this paper, we consider some inequalities in w-X involving the mean oscillation and the maximal function of a martingale. The main results give necessary and sufficient conditions for the inequalities to be valid.

KW - Banach function space

KW - Inequality

KW - Martingale

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On some martingale inequalities for mean oscillations in weak spaces

Abstract

Keywords

ASJC Scopus subject areas

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