Besov spaces, multipliers and univalent functions
For \(1\leq p<\infty\), let \(B^p\) denote the Besov spaces of holomorphic functions in the unit disk, and let \(B\) denote the Bloch space. The authors consider \(M(B^p,B^q)\) and \(M(B^p,B)\), the spaces of multipliers from \(B^p\) to \(B^q\) and \(B\), respectively, for \(1\leq p,q<\infty\), and they find characterizations of these spaces, without use of capacity. The authors investigate ``which functions of certain important types (lacunary series, univalent functions, `modified' inner functions) are to be found in the spaces \(M(B^p,B^q)\)''. Studying lacunary series as \(M(B^p,B^q)\) members, the authors are able to give a negative answer to the problem stated in [\textit{N. Zorboska}, in: More progresses in analysis. Proceedings of the 5th international ISAAC congress, Catania, Italy, July 2005. Hackensack, NJ: World Scientific. 387--396 (2009; Zbl 1192.47026)].
scientific article; zbMATH DE number 6214961
scientific article