Abstract
AbstractA general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebraW(C,ℓ1)($\mathbb{R}$d). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from theHpHardy space toLp(orHp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.
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