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Mean and Almost Everywhere Convergence of Fourier–Neumann Series

✍ Scribed by Óscar Ciaurri; José J. Guadalupe; Mario Pérez; Juan L. Varona

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 162 KB
Volume: 236
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6442

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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