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Wiener amalgams, Hardy spaces and summability of Fourier series

Published online by Cambridge University Press:  01 September 2008

FERENC WEISZ
FERENC WEISZ*
Affiliation:
Department of Numerical Analysis, Eötvös L. University, Pázmány P. sétány 1/C., H-1117 Budapest, Hungary. e-mail: weisz@numanal.inf.elte.hu
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Abstract

A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(d). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 419 - 442
Copyright
Copyright © Cambridge Philosophical Society 2008

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