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Characterizations of some properties on weighted modulation and Wiener amalgam spaces. (English) Zbl 1427.42028

Summary: In this paper, we characterize some properties on weighted modulation and Wiener amalgam spaces by the corresponding properties on weighted Lebesgue spaces. As applications, we obtain sharp conditions for product inequalities, convolution inequalities, and embedding on weighted modulation and Wiener amalgam spaces. By a unified approach different from others we give a complete answer to the question of finding sharp conditions of certain relations on weighted modulation and Wiener amalgam spaces.

MSC:

42B35 Function spaces arising in harmonic analysis
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47G30 Pseudodifferential operators
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