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Atomic, molecular and wavelet decomposition of generalized 2-microlocal Besov spaces. (English) Zbl 1207.42020

This paper deals with the 2-microlocal Besov spaces previously considered by the author in [Rev. Mat. Complut. 22, 227–251(2009; Zbl 1166.42011)], in that case with variable integrability. The main results refer to the atomic and molecular representations of elements in such a space in the corresponding discrete 2-microlocal Besov space. Also a wavelet decomposition is obtained and used to prove the invariance of these spaces under pseudo-differential operators of order 0.

MSC:

42B35 Function spaces arising in harmonic analysis
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47G30 Pseudodifferential operators

Citations:

Zbl 1166.42011
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