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

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(L-1, l(q))(R) and f is almost everywhere locally bounded, or f is an element of W(L-p, l(q))(R) (1 < p < infinity, 1 <= q < infinity), then strong theta-summability holds at each Lebesgue point of f. The analogous results are given for Fourier series, too.