Norms of Composition Operators from Weighted Harmonic Bloch Spaces into Weighted Harmonic Zygmund Spaces

Abstract

This article examines the norms of composition operators from the weighted harmonic Bloch space BHλ,0<λ<∞ to the weighted harmonic Zygmund space ZHβ,0<β<∞. The critical norm is on the open unit disk. We first give necessary and sufficient conditions where the composition operator between BHλ and ZHβ is bounded. Secondly, we will study the compactness case of the composition operator between BHλ and ZHβ. Finally, we will estimate the essential norms of the composition operator between BHλ and ZHβ.