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TOEPLITZ OPERATORS BETWEEN FOCK SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 2 / October 2015
- Published online by Cambridge University Press:
- 02 June 2015, pp. 316-324
- Print publication:
- October 2015
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- Article
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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.
