Dörfler, Monika; Feichtinger, Hans G.; Gröchenig, Karlheinz Compactness criteria in function spaces. (English) Zbl 1017.46014 Colloq. Math. 94, No. 1, 37-50 (2002). The well-known compactness criterion in \(L_2 ({\mathbb R}^n)\) can be reformulated in terms of the continuous wavelet transform \[ W_g f (x,s) = s^{- \frac{n}{2}} \int_{{\mathbb R}^n} f(t) g\biggl( \frac{t-x}{s}\biggr) dt, \quad x \in {\mathbb R}^n, s >0. \] The authors extend this observation to abstract coorbit spaces (Theorem 4). They apply the outcome to some concrete distinguished examples: modulation spaces in \({\mathbb R}^n\), spaces of type \(B^s_{pq} ({\mathbb R}^n)\), \(F^s_{pq} ({\mathbb R}^n)\), and Bargman-Fock spaces on \({\mathbb C}^n\). Reviewer: Hans Triebel (Jena) Cited in 2 ReviewsCited in 8 Documents MSC: 46B50 Compactness in Banach (or normed) spaces 42B35 Function spaces arising in harmonic analysis 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:function spaces; wavelet transform; Besov spaces; Triebel-Lizorkin spaces PDFBibTeX XMLCite \textit{M. Dörfler} et al., Colloq. Math. 94, No. 1, 37--50 (2002; Zbl 1017.46014) Full Text: DOI arXiv