In this paper we study properties of Toeplitz operators on weighted Bergman spaces of bounded strongly pseudoconvex domains. We prove that a Toeplitz operator built using a weighted Bergman kernel of weight β and integrating against a measure μ maps continuously a weighted Bergman space Ap1α1 (D) into Ap2α2 (D) if and only if μ is a (λ, γ)-skew Carleson measure, where λ = 1 + 1/p1 - 1/p2 and γ = 1 l (β + α1/p1 - α2/p2). This generalizes results obtained by Pau and Zhao on the unit ball, and by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on strongly pseudoconvex domains.
Toeplitz operators and skew carleson measures for weighted bergman spaces on strongly pseudoconvex domains
Mongodi S.;
2020-01-01
Abstract
In this paper we study properties of Toeplitz operators on weighted Bergman spaces of bounded strongly pseudoconvex domains. We prove that a Toeplitz operator built using a weighted Bergman kernel of weight β and integrating against a measure μ maps continuously a weighted Bergman space Ap1α1 (D) into Ap2α2 (D) if and only if μ is a (λ, γ)-skew Carleson measure, where λ = 1 + 1/p1 - 1/p2 and γ = 1 l (β + α1/p1 - α2/p2). This generalizes results obtained by Pau and Zhao on the unit ball, and by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on strongly pseudoconvex domains.File in questo prodotto:
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