Smoothness and Function Spaces Generated by Homogeneous Multipliers
Copyright policy )Smoothness and Function Spaces Generated by Homogeneous Multipliers
Differential operators generated by homogeneous functionsψof an arbitrary real orders>0(ψ-derivatives) and related spaces ofs-smooth periodic functions ofdvariables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas forψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.
Besov spaces, Triebel-Lizorkin spaces, QA1-939, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematics
Besov spaces, Triebel-Lizorkin spaces, QA1-939, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematics
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