Kempka, Henning Atomic, molecular and wavelet decomposition of generalized 2-microlocal Besov spaces. (English) Zbl 1207.42020 J. Funct. Spaces Appl. 8, No. 2, 129-165 (2010). 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) Cited in 32 Documents 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 Keywords:Besov spaces; microlocal spaces; wavelets; atomic decomposition; molecular decomposition Citations:Zbl 1166.42011 PDFBibTeX XMLCite \textit{H. Kempka}, J. Funct. Spaces Appl. 8, No. 2, 129--165 (2010; Zbl 1207.42020) Full Text: DOI