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Weierstrass and Picard summability of more-dimensional Fourier transforms

Abstract It is proved that the maximal operator of the Weierstrass and Picard summability means of a tempered distribution is bounded from Hp(ℝd) to Lp(ℝd) 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 ∈ L1(ℝd) converge a.e. to f. Similar results are shown for conjugate functions and for Fourier series.