On a generalized Möbius invariant function space

In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains Bα, Bαp, BMOApα, and F(p,pα−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.