Pointwise Summability of Gabor Expansions |
| |
Authors: | Ferenc Weisz |
| |
Institution: | (1) Department of Numerical Analysis, Eötvös Loránd University, H-1117 Budapest, Pázmány P. Sétány 1/C |
| |
Abstract: | 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 f∈L
1 or, more generally, when f∈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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|