Weierstrass and Picard summability of more-dimensional Fourier transforms

摘要

It is proved that the maximal operator of the Weierstrass and Picard summability means of a tempered distribution is bounded from H_p(R~d) to L_p(R~d) for all 0 < p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the summability means of a function f ∈ L_1(R~d ) converge a.e. to f. Similar results are shown for conjugate functions and for Fourier series.