Toeplitz Operators and Skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains

2019/05/29 by Abate, Marco, Mongodi, Samuele, Raissy, Jasmin · 1 citation
#32A25 #32A36 (primary) #32Q45 #32T15 #46E15 #46E22 #47B35 (secondary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.13056

Abstract

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in ℂn. In particular we prove that a Toeplitz operator built using as kernel a weighted Bergman kernel of weight β and integrating against a measure μ maps continuously (when β is large enough) a weighted Bergman space Ap1α1(D) into a weighted Bergman space Ap2α2(D) if and only if μ is a (λ,γ)-skew Carleson measure, where λ=1+(1)/(p1)-(1)/(p2) and γ=\frac1λ(β+(α1)/(p1)-(α2)/(p2)). This theorem generalizes results obtained by Pau and Zhao on the unit ball, and extends and makes more precise results obtained by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on bounded strongly pseudoconvex domains.

Cited by

• A note for Carleson measure on bounded ℂ-convex domains

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