On a generalized Möbius invariant function space

In this paper, we introduce a new class of generalized M & ouml;bius function space of analytic functions in the unit disk, that contains Zi alpha, B p alpha , BMOA alpha p , 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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.