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Sharp embedding relations between local Hardy and \(\alpha\)-modulation spaces. (English) Zbl 1488.42114

An \(\alpha\)-modulation space is a generalization of a modulation space and it links modulation spaces and Besov spaces by the parameter \(\alpha\). But \(\alpha\)-modulation spaces can not be obtained by interpolation between modulation spaces and Besov spaces. In this paper the authors give optimal embedding relation between \(\alpha\)-modulation spaces and local Hardy spaces (or Sobolev spaces).

MSC:

42B35 Function spaces arising in harmonic analysis
42B30 \(H^p\)-spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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