Lebesgue points and restricted convergence of Fourier transforms and Fourier series
2016 ◽
Vol 15
(01)
◽
pp. 107-121
◽
Keyword(s):
In this paper, a general summability method of multi-dimensional Fourier transforms, the so-called [Formula: see text]-summability, is investigated. It is shown that if [Formula: see text] is in a Herz space, then the summability means [Formula: see text] of a function [Formula: see text] converge to [Formula: see text] at each modified Lebesgue point, whenever [Formula: see text] and [Formula: see text] is in a cone. The same holds for Fourier series. Some special cases of the [Formula: see text]-summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, Cesàro, de la Vallée-Poussin, Rogosinski and Riesz summations.
2008 ◽
Vol 145
(2)
◽
pp. 419-442
◽
Keyword(s):
Keyword(s):
2011 ◽
Vol 379
(2)
◽
pp. 910-929
◽