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A relation between two kinds of norms for martingales

In: Mathematica Slovaca, vol. 65, no. 5
Masato Kikuchi

Details:

Year, pages: 2015, 1165 - 1180
Keywords:
martingale, Banach function space, rearrangement-invariant function space, norm inequality
About article:
Let $X$ be a Banach function space over a nonatomic probability space $Ω$ and let $\mathcal{M}u$ denote the collection of all uniformly integrable martingales on $Ω$. For $f=(fn)_{n \in \mathbb{Z}+}\in \mathcal{M}u$, let $\mathcal{M}{f}$ denote the maximal function of $f$, and let $f$ denote the almost sure limit of $f$. We give some necessary and sufficient conditions for $X$ to have the property that if $f,g \in \mathcal{M}u$ and $|M{g}|X ≤ |M{f}|X$, then $|g|X ≤ C|f|X$.
How to cite:
ISO 690:
Kikuchi, M. 2015. A relation between two kinds of norms for martingales. In Mathematica Slovaca, vol. 65, no.5, pp. 1165-1180. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0080

APA:
Kikuchi, M. (2015). A relation between two kinds of norms for martingales. Mathematica Slovaca, 65(5), 1165-1180. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0080
About edition:
Published: 1. 10. 2015