Abstract
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, l∞) to W(Lp, l∞). This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W(L1, l∞) ⊃ L1.
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