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 B α , B α p , BMOA p α , and F ( p , p α − 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.