Abstract
Under some weak conditions on θ, it was verified in [21, 17] that the maximal operator of the l1-θ-means of a tempered distribution is bounded from Hp(ℝd) to Lp(ℝd) for all d/(d + α) < p ≤ ∞, where 0 < α ≤ 1 depends only on θ. In this paper, we prove that the maximal operator is bounded from Hd/(d+α)(ℝd) to the weak Ld/(d+α)(ℝd) space. The analogous result is given for Fourier series, as well. Some special cases of the l1-θ-summation are considered, such as the Weierstrass, Picard, Bessel, Fejer, de La Vallee-Poussin, Rogosinski and Riesz summations.
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