A \(\varphi\)-transform result for spaces with dominating mixed smoothness properties
The main result of this note is a sequence space characterization of certain Banach spaces with dominating mixed smoothness properties, in the spirit of the work of \textit{M. Frazier} and \textit{B. Jawerth} [J. Funct. Anal. 93, No. 1, 34-170 (1990; Zbl 0716.46031)]. More precisely, the author describes the corresponding Triebel-Lizorkin spaces [cf. the book by \textit{H.-J. Schmeisser} and \textit{H. Triebel}: ``Topics in Fourier analysis and function spaces'' (1987; Zbl 0661.46024) for details on these spaces] in terms of appropriate Fourier decompositions and derives therefrom the fact that these spaces are retracts of certain solid sequence spaces, for the full range of parameters, i.e., indices \(p,q\) down to \(0\). Although the general approach follows the lines of previous work the details are technically quite involved.
Banach spaces with dominating mixed smoothness properties
scientific article; zbMATH DE number 1140111
scientific article