Restricted Summability of Fourier Transforms and Local Hardy Spaces  

作　　者：Ferenc WEISZ 

机构地区：[1]Department of Numerical Analysis, Etvs L. University

出　　处：《Acta Mathematica Sinica,English Series》2010年第9期1627-1640,共14页数学学报（英文版）

基　　金：Supported by the Hungarian Scientific Research Funds (OTKA) No. K67642

摘　　要：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, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.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, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.

关 键 词：Wiener amalgam spaces local Hardy spaces 0-summability of Fourier transforms atomic decomposition 

分 类 号：O174.22[理学—数学]