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Mean Convergence of Vector-valued Walsh Series

✍ Scribed by Jörg Wenzel

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 229 KB
Volume: 162
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19931620109

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✦ Synopsis

Given any Banach space X, let L: denote the Banach space of all measurable functions f : [0, 11 + X for which llfllz:=( Ilf(t)ll'dt)l'z is finite. We show that X is a UMD-space (see [l]) if and only if lim [ I f -SJj)llZ = O for all EL.:, n where n-1 SnCnl= C (h wi>wi i = o

is the n-th partial sum associated with the Walsh system (wi).

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