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On Hankel operators between Fock spaces

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In this paper, we characterize the mapping properties of Hankel operators $$H_{g}$$ and $$ H_{\overline{g}}$$ associated to some restricted function g on the complex space $$\mathbf{C}^n$$. We, in particular, describe… Click to show full abstract

In this paper, we characterize the mapping properties of Hankel operators $$H_{g}$$ and $$ H_{\overline{g}}$$ associated to some restricted function g on the complex space $$\mathbf{C}^n$$. We, in particular, describe the boundedness and compactness of operators $$H_{g}$$ and $$ H_{\overline{g}}$$ acting between Fock spaces in terms of Berezin transforms of their inducing function g. Our results extend a recent work of Z. Hu and E. Wang and fills the remaining gap when the largest Fock spaces are taken into account. And for $$1 \le s, p \le \infty $$, we also obtain the characterization on $$IMO^{s,p}$$, the space of functions satisfying an integral condition for the mean oscillation, via Berezin transform.

Keywords: hankel operators; operators fock; fock spaces

Journal Title: Banach Journal of Mathematical Analysis
Year Published: 2020

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