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Hankel Operators Between Fock Spaces

  • Zhangjian Hu
  • Ermin Wang
Article

Abstract

In this paper, we introduce a function space integrable mean oscillation (IMO) on \({\mathbb {C}}^n\). With IMO, for all possible \(1\le p,q<\infty \) we characterize those symbols f on \( {\mathbb {C}}^n\) for which the Hankel operators \(H_{f}\) and \( H_{\overline{f}}\) are simultaneously bounded (or compact) from Fock space \(F^{p}_{\alpha }\) to Lebesgue space \(L^{q}_{\alpha }\). As a consequence we obtain all holomorphic functions f for which the Hankel operators \(H_{\overline{f}}\) are bounded (or compact) from \(F^{p}_{\alpha }\) to \(L^{q}_{\alpha }\).

Keywords

Fock spaces IMO spaces Hankel operators 

Mathematics Subject Classification

Primary 47B38 Secondary 32A37 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou UniversityHuzhouChina
  2. 2.School of Mathematics and StatisticsLingnan Normal UniversityZhanjiangChina

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