Product(α1,α2)-modulation spaces Dedicated to the Memory of Michel Marias  

作　　者：Galatia Cleanthous Athanasios G.Georgiadis 

机构地区：[1]Department of Mathematics and Statistics,National University of Ireland,Maynooth W 23 F 2K8,Ireland [2]Faculty of Engineering,Mathematics and Science,Trinity College of Dublin,Dublin D02 PN40,Ireland

出　　处：《Science China Mathematics》2022年第8期1599-1640,共42页中国科学：数学（英文版）

基　　金：supported by University of Cyprus and New Function Spaces in Harmonic Analysis and Their Applications in Statistics(Individual Grant)。

摘　　要：We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.

关 键 词：product(α1 α2)-modulation space product space mixed smoothness short time Fourier transform EMBEDDING dual tight frame discrete decomposition 

分 类 号：O174[理学—数学]