Abstract
We study big Hankel operators acting on vector-valued Fock spaces with radial weights in mathbb {C}^d. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.
Highlights
IntroductionThe classical Fock space (or, the Segal–Bargmann space) has a long and celebrated history and its origins are found in quantum mechanics
The classical Fock space has a long and celebrated history and its origins are found in quantum mechanics
Seip and Youssfi [14] studied big Hankel operators with anti-holomorphic symbols acting on a large class of scalar Fock spaces with radial weights subject to a mild smoothness condition
Summary
The classical Fock space (or, the Segal–Bargmann space) has a long and celebrated history and its origins are found in quantum mechanics. The objective of our paper is to study big Hankel operators with anti-analytic symbols on generalized vector-valued Fock spaces. Seip and Youssfi [14] studied big Hankel operators with anti-holomorphic symbols acting on a large class of scalar Fock spaces with radial weights subject to a mild smoothness condition (see below). Using their sharp estimates for the reproducing kernel, we investigate this class of operators in the vectorvalued setting and define adequate versions of Bloch, Besov spaces and of mean oscillation.
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