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Weighted Inequalities for Vector Operators on Martingales

✍ Scribed by S.A. Tozoni

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 596 KB
Volume: 191
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1128

No coin nor oath required. For personal study only.

✦ Synopsis

Sufficient conditions are given to get weighted inequalities between two maximal operators on Banach valued regular martingales. As an application we obtain generalizations with weights of the inequalities in the definitions of UMD- and MT-Banach spaces and weighted estimates for the vector valued square function operator. We also obtain results for Haar and Walsh series. In particular it is shown that (L_{x}^{p})-convergence of the Walsh-Fourier series characterizes UMD spaces. 1995 Academic Press. Inc.

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