SCHATTEN CLASS HANKEL OPERATORS ON THE SEGAL-BARGMANN SPACE AND THE BERGER-COBURN PHENOMENON

SCHATTEN CLASS HANKEL OPERATORS ON THE SEGAL-BARGMANN SPACE AND THE BERGER-COBURN PHENOMENON

We give a complete characterization of Schatten class Hankel operators Hf acting on weighted Segal-Bargmann spaces F2(φ) using the notion of integral distance to analytic functions in Cn and Hörmander's ∂-theory. Using our characterization, for f ∈ L∞ and 1 < p < ∞, we prove that Hf is i...

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Bibliographic Details
Main Authors: Hu, Z. (Author), VIRTANEN, J.A (Author)
Format: Article
Language:English
Published: American Mathematical Society 2022
Subjects:
Hankel operator
Schatten class
Segal-Bargmann space
Online Access:View Fulltext in Publisher
Description
Summary:We give a complete characterization of Schatten class Hankel operators Hf acting on weighted Segal-Bargmann spaces F2(φ) using the notion of integral distance to analytic functions in Cn and Hörmander's ∂-theory. Using our characterization, for f ∈ L∞ and 1 < p < ∞, we prove that Hf is in the Schatten class Sp if and only if H f ∈ Sp, which was previously known only for the Hilbert-Schmidt class S2 of the standard Segal-Bargmann space F2(φ) with φ(z) = α|z|2. © 2022 American Mathematical Society.
ISBN:00029947 (ISSN)
DOI:10.1090/tran/8638

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