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, if f is in the Wiener amalgam space W(L1,lq)(R) and f is almost everywhere locally bounded, or f∈W(Lp,lq)(R) (1<p<∞,1≤q<∞), then strong θ-summability holds at each Lebesgue point of f. The analogous results are given for Fourier series, too.