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TOEPLITZ OPERATORS BETWEEN FOCK SPACES

Part of: Holomorphic functions of several complex variables Special classes of linear operators

Published online by Cambridge University Press:  02 June 2015

JIN LU  and
XIAOFEN LV
JIN LU
Affiliation:
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, PR China email [email protected]
XIAOFEN LV*
Affiliation:
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, PR China email [email protected]
*
✉[email protected]
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Abstract

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Given a positive Borel measure ${\it\mu}$ on the $n$-dimensional Euclidean space $\mathbb{C}^{n}$, we characterise the boundedness (and compactness) of Toeplitz operators $T_{{\it\mu}}$ between Fock spaces $F^{\infty }({\it\varphi})$ and $F^{p}({\it\varphi})$ with $0<p\leq \infty$ in terms of $t$-Berezin transforms and averaging functions of ${\it\mu}$. Our result extends recent work of Mengestie [‘On Toeplitz operators between Fock spaces’, Integral Equations Operator Theory78 (2014), 213–224] and others.

Keywords

Toeplitz operatorFock spacet-Berezin transforms

MSC classification

Primary: 47B38: Operators on function spaces (general)
Secondary: 32A36: Bergman spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 316 - 324
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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