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BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL

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

Published online by Cambridge University Press:  05 June 2015

MAŁGORZATA MICHALSKA  and
PAWEŁ SOBOLEWSKI
MAŁGORZATA MICHALSKA
Affiliation:
Instytut Matematyki UMCS, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland email malgorzata.michalska@umcs.pl
PAWEŁ SOBOLEWSKI*
Affiliation:
Instytut Matematyki UMCS, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland email pawel.sobolewski@umcs.eu
*
✉pawel.sobolewski@umcs.eu
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Abstract

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Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

Keywords

Toeplitz operatorsHankel operatorsweighted Bergman spaces

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 32A36: Bergman spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 2 , October 2015 , pp. 237 - 249
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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