Schneider, Georg Compact subsets of spaces of holomorphic functions. (English) Zbl 1097.46504 Acta Math. Acad. Paedagog. Nyházi. (N.S.) 21, 71-77 (2005). Summary: M. Dörfler, H. Feichtinger and K. Gröchenig [Colloq.Math.94, No. 1, 37–50 (2002; Zbl 1017.46014)] investigated compactness criteria in function spaces for the case of general coorbit spaces. These methods cannot be easily adapted for the spaces \(F_m\) and the Bergman spaces \(B^2(\Omega)\). We will be able to derive a generalization of the above mentioned result to the spaces \(F_m\) and \(B^2(\Omega)\). Furthermore, we will be able to derive a sufficient compactness condition for subsets \(A\) of the Fock space in terms of the Taylor-expansion of the functions \(f\in A\). We will introduce increasing norm-spaces, which are a natural generalization of the above mentioned spaces. The main resultfor the spaces \(F_m\) and \(B^2(\Omega)\) will follow from this result. MSC: 46B50 Compactness in Banach (or normed) spaces Keywords:Fock space; Bergman space; increasing norm space Citations:Zbl 1017.46014 PDFBibTeX XMLCite \textit{G. Schneider}, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 21, 71--77 (2005; Zbl 1097.46504) Full Text: EuDML EMIS