Carleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are defined using imbeddings into Lebesgue classes via radial derivatives. The measures, some of which are infinite, are characterized in terms of Berezin transforms and Bergman-metric balls, extending results for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view wit...

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into $b^{q}_{\beta}$, Bloch $b^{\infty}_{\beta} $ or space functions $h^{\infty}$, allowing exponents to be different. These can viewed as generalizations projections.

Let φ and ψ be holomorphic maps on such that φ( ) ⊂ . Let Cφ,Mψ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces AβN to Bloch-type spaces. In fact, we prove that these operators map AβN compactly into Bloch-type spaces if and only if they map A β...

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.