Almost everywhere summability of Fourier series with indication of the set of convergence

2016 ◽  
Vol 100 (1-2) ◽  
pp. 139-153 ◽  
Author(s):  
R. M. Trigub
Keyword(s):  
Fourier Series ◽  
Almost Everywhere ◽  
Summability Of Fourier Series ◽  
Almost Everywhere Summability

Wiener amalgams, Hardy spaces and summability of Fourier series

2008 ◽  
Vol 145 (2) ◽  
pp. 419-442 ◽  
Author(s):  
FERENC WEISZ
Keyword(s):  
Fourier Series ◽  
Hardy Spaces ◽  
Summability Method ◽  
Wiener Amalgam Spaces ◽  
Almost Everywhere ◽  
Convergence Results ◽  
Special Cases ◽  
Summability Of Fourier Series ◽  
Amalgam Spaces ◽  
General Summability

AbstractA general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebraW(C,ℓ1)($\mathbb{R}$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 theHpHardy space toLp(orHp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

scholarly journals Maximal transference and summability of multilinear Fourier series

2006 ◽  
Vol 80 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Loukas Grafakos ◽  
Petr Honzík
Keyword(s):  
Fourier Series ◽  
Multilinear Operators ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Transference Theorem ◽  
Almost Everywhere Summability

AbstractWe obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m–linear Fourier series. We formulate conditions for the convergence of multilinear series and we investigate certain kinds of summation.

GENERALIZED MEANS AND THE SUMMABILITY OF FOURIER SERIES

1931 ◽  
Vol os-2 (1) ◽  
pp. 207-229 ◽  
Author(s):  
L. S. BOSANQUET ◽  
E. H. LINFOOT
Keyword(s):  
Fourier Series ◽  
Summability Of Fourier Series
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