Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces

Abstract

We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, iffis in the Wiener amalgam spaceW(L1,lq)(R)andfis almost everywhere locally bounded, orf∈W(Lp,lq)(R) (1<p<∞,1≤q<∞), then strongθ-summability holds at each Lebesgue point off. The analogous results are given for Fourier series, too.

On Exponential Summability of Rectangular Partial Sums of Double Trigonometric Fourier Series

“…The results on strong summability and approximation by trigonometric Fourier series have been extended for several other orthogonal systems, see Schipp [23,24,25], Leindler [14,15,16,17], Totik [26,27,28,29], Goginava, Gogoladze [5,6], Goginava, Gogoladze, Karagulyan [7], Gat, Goginava, Karagulyan [3,4], Weisz [30]- [33].…”