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.
Reviewer: Joan Cerdà (Barcelona)
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 |