On a generalized Möbius invariant function space

Abstract

In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains $B_{\alpha }$, $B_{\alpha }^p$, ${\text{BMOA}}_p^{\alpha }$, and $F(p,p\alpha -2,s)$ as particular cases. We study several basic properties of such new spaces and also characterize these spaces via Carleson-type measures. As for some applications, we study the corresponding little-o spaces, as well as establish several embedding relations of these new spaces with Bloch-type spaces. Our result generalizes an early work of Zhu in 2007.