Characterization of Schatten-class Hankel operators on weighted Bergman spaces
نویسندگان
چکیده
منابع مشابه
Schatten Class Hankel Operators on the Bergman Spaces of Strongly Pseudoconvex Domains
In this paper, we characterize holomorphic functions / such that the Hankel operators Hj are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > In , Hj is in the Schatten class Sp if and only if / is in the Besov space Bp ; for p < In , Hj is in the Schatten class Sp if and only if / = constant.
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Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2016
ISSN: 0012-7094
DOI: 10.1215/00127094-3627310