Canonical divisors in Bergman spaces can be found as solutions of extremal problems. We derive a formula for certain extremal functions in the weighted Bergman spaces Aα for α > −1 and 1 ≤ p <∞. This leads to a study of the zeros of a specific family of hypergeometric functions.

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...

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize which are hermitian and those complex symmetric with respect to family conjugations. As it turns out, enhanced by symmetry must be bounded. Hermitian, unitary proven an adapted highly relevant conjugation. classify linear fractional functions give rise bounded operators. end paper natu...

We give examples of composition operators CΦ on H(D) showing that the condition ‖Φ‖∞ = 1 is not sufficient for their approximation numbers an(CΦ) to satisfy limn→∞[an(CΦ)] √ n = 1, contrary to the 1-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Ampère capacity of the image of Φ. Key-words : approximation numbers; Bergman space; bidisk; co...

We characterize those measures μ for which the Hardy-Orlicz (resp. weighted Bergman-Orlicz) space HΨ1 (resp. AΨ1 α ) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2 ( BN ,μ ) (resp. LΨ2 (BN ,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1 ⊂ LΨ j for i, j ∈ {1,2}, and such that Ψ2/Ψ1 is non-decreasing. We apply our result to the charact...