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In this paper, for 1 ≤ p < ∞ , we provide several descriptions of Schatten p -class Hankel operators H f and H f ‾ on the weighted Bergman space A ω 2 , in terms of a certain global and local mean oscillation of the symbol f ∈ L ω 2 , provided ω is in a class of regular weights. The approaches applied to rely on several classical methods, and simultaneously rely on a novel but more convenient construction associated with the atomic decomposition of A ω 2. [ABSTRACT FROM AUTHOR]

In this paper, the boundedness and compactness of the difference of composition-differentiation operators D φ − D ψ acting from Hardy spaces H p to weighted Bergman spaces A α q are completely characterized for all 0 < p , q < ∞. [ABSTRACT FROM AUTHOR]

In this paper we consider the hyponormality of Toeplitz operators T Φ on the weighted Bergman space with matrix-valued circulant symbols Φ. We give a necessary and sufficient condition for the hyponormality of T Φ with such a symbol Φ under some constraint on the entries of the matrix. [ABSTRACT FROM AUTHOR]

Let G be a finite pseudoreflection group and Ω ⊆ C d be a bounded domain which is a G -space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of Ω and Ω / G using invariant theory and representation theory of G. This, in turn, provides techniques to study algebraic properties of Toeplitz operators on the weighted Bergman space on Ω / G. We specialize on the generalized zero-product problem and characterization of commuting pairs of Toeplitz operators. As a consequence, more intricate results on Toeplitz operators on the weighted Bergman spaces on some specific quotient domains (namely symmetrized polydisc, monomial polyhedron, Rudin's domain) have been obtained. [ABSTRACT FROM AUTHOR]

We use the resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces. [ABSTRACT FROM AUTHOR]

Abstract: The boundedness and compactness of weighted iterated radial operators between different weighted Bergman spaces on the unit ball are characterized here. [Copyright &y& Elsevier]

Abstract: We characterize the compactness of differences of weighted composition operators from the weighted Bergman space , 0< p <∞, α >−1, to the weighted-type space of analytic functions on the open unit disk in terms of inducing symbols and . For the case 1< p <∞ we find an asymptotically equivalent expression to the essential norm of these operators. [Copyright &y& Elsevier]

Abstract: The boundedness of the composition operator from the weighted Bergman space to, recently introduced by this author, the nth weighted-type space on the upper half-plane are characterized here. [Copyright &y& Elsevier]

Abstract: Let be a bounded symmetric domain, the class of all holomorphic functions on and . Operator norm of the multiplication operator on the weighted Bergman space , as well as of weighted composition operator from to a weighted-type space are calculated. [Copyright &y& Elsevier]

Abstract: Let be the class of all holomorphic functions on the set and . We calculate operator norms of the multiplication operators , on the weighted Bergman space , as well as on the Hardy space , where X is the unit polydisk or the unit ball in . We also calculate the norm of the weighted composition operator from the weighted Bergman space , and the Hardy space , to a weighted-type space on the unit polydisk. [Copyright &y& Elsevier]

Let D be a bounded symmetric domain and Σ be the Shilov boundary of D. For λ∈W, the Wallach set, and a nonnegative integer l, we study the weighted Bergman space Aλ2(D) and the weighted Bergman–Sobolev space A2,λ,l(D). For 0<ρ<1 we obtain exact values of the Gel''fand and linear N-widths of A2,λ,l(D) in C(ρΣ). We also obtain the Bernstein N-widths of the Hardy–Sobolev space H∞,l(D) in Aλ2(ρD). [Copyright &y& Elsevier]