We use induction and interpolation techniques to prove that a composition operator induced by a map φ is bounded on the weighted Bergman space Aα(H) of the right half-plane if and only if φ fixes ∞ non-tangentially, and has a finite angular derivative λ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by λ.

We describe new Banach (not C∗ !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball B, where n > 2. For n = 2 all these algebras collapse to the single C∗-algebra generated by Toeplitz operators with quasi-parabolic symbols. As a by-product, we describe the situations when the product of mutually commuting Toeplitz operators is a To...

We study when weighted composition operators Cφ,ψ acting between weighted Bergman spaces of infinite order are power bounded resp. uniformly mean ergodic.

Let Ω be a bounded pseudoconvex domain in C N , φ, ψ two positive functions on Ω such that − logψ,− log φ are plurisubharmonic, z ∈ Ω a point at which − log φ is smooth and strictly plurisubharmonic, and M a nonnegative integer. We show that as k → ∞, the Bergman kernels with respect to the weights φkψM have an asymptotic expansion KφkψM (x, y) = kN πNφ(x, y)kψ(x, y)M ∞ ∑ j=0 bj(x, y) k −j , b0...

Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...

In this paper, we focus on the weighted Bergman spaces Aφp in D with φ∈W0. We first give characterizations of those finite positive Borel measures µ such that embedding Aφp⊂Lμq is bounded or compact for 0<p,q<∞. Then describe Toeplitz operators Tμ from one space to another Aφq all possible Finally, characterize Schatten class Aφ2.

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.