Pointwise Summability of Gabor Expansions

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• 作者：Ferenc Weisz
• 关键词：Wiener amalgam spaces ; Herz spaces ; θ ; summability ; Gabor expansions ; Gabor frames ; Time ; frequency analysis ; Hardy ; Littlewood inequality
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2009
• 出版时间：August, 2009
• 年：2009
• 卷：15
• 期：4
• 页码：463-487
• 全文大小：426.5 KB

文摘

A general summability method, the so-called θ-summability method is considered for Gabor series. It is proved that if the Fourier transform of θ is in a Herz space then this summation method for the Gabor expansion of f converges to f almost everywhere when fW12;L ₁ or, more generally, when fW12;W(L ₁,ℓ _∞) (Wiener amalgam space). Some weak type inequalities for the maximal operator corresponding to the θ-means of the Gabor expansion are obtained. Hardy-Littlewood type maximal functions are introduced and some inequalities are proved for these.