Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces. (2nd September 2015)

• Record Type: Journal Article
• Authors: Weisz, Ferenc
• Other Names: Popescu Gelu Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-09-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/420750
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, iff is in the Wiener amalgam spaceW ( L 1, l q ) ( R ) andf is almost everywhere locally bounded, orf ∈ W ( L p, l q ) ( R ) ( 1 < p < ∞, 1 ≤ q < ∞ ), then strongθ -summability holds at each Lebesgue point off . The analogous results are given for Fourier series, too.