We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of C n . Let 0 < p, s < +∞,−n−1 < q < +∞, q + s > −1 and α ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operator Wψ,φ induced by φ and ψ to be bounded and compact between the space F (p, q, s) and α-Bloch space β.

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...

We provide a full characterization in terms of the six parameters involved boundedness all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with weights on unit ball Rn. These some sense generalize projections. To obtain necessity conditions, we use technique that heavily depends precise inclusion relations and Bloch spaces...

Let 0 ≤ α < 1. Denote the open unit polydisk in C by ∆. We obtain a purely function-theoretic condition characterizing the holomorphic self-maps of ∆ that induce bounded composition operators on (1−α)-Bloch spaces, which we define on ∆. As a consequence, we extend Madigan’s characterization of bounded composition operators on analytic α-Lipschitz spaces over ∆ for 0 < α < 1 to an analogous char...