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Fourier multipliers on Triebel-Lizorkin-type spaces. (English) Zbl 1248.42016

First, the authors recall new definitions of Triebel-Lizorkin-type spaces and Triebel-Lizorkin-Hausdorff spaces. Then they study mapping properties of Fourier multipliers, with symbols satisfying a generalized Hörmander’s condition, on such spaces. As an application of their results, they give new direct proofs of the Sobolev embedding theorems on these spaces.

MSC:

42B15 Multipliers for harmonic analysis in several variables
42B35 Function spaces arising in harmonic analysis
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