Local Hardy spaces and summability of Fourier transforms |
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Authors: | Ferenc Weisz |
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Institution: | aDepartment of Numerical Analysis, Eötvös L. University, H-1117 Budapest, Pázmány P. sétány 1/C, Hungary |
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Abstract: | New Wiener amalgam spaces are introduced for local Hardy spaces. 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 is bounded from the amalgam space to W(Lp,ℓ∞). This implies the almost everywhere convergence of the θ-means for all f W(L1,ℓ∞) L1. |
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Keywords: | Wiener amalgam spaces Local Hardy spaces θ -summability of Fourier transforms Atomic decomposition |
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