where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

We characterize the symbols φ for which there exists a weight w such that weighted composition operator MwCφ is compact on Bergman space Bα2. also bounded but not compact. investigate when Hilbert-Schmidt

We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

In this paper we study the weighted Bergman-Orlicz spaces Aα. Among other properties we get that Aα is a Banach space with the Luxemburg norm. We show that the set of analytic polynomials is dense in Aα. We also study compactness and continuity of the composition operator on Aα. Mathematics Subject Classification: 46E30, 47B33

In the paper, we discuss on the egg domains: Ω a = ξ = (z, w) ∈ C n+m : z ∈ C n , w ∈ C m , |z| 2 + |w| 2/a < 1 , 0 < a ≤ 2. We show that Gleason's problem can be solved in the weight Bergman space on the egg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier th...