Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of

Dieudonne Agbor

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-11

Abstract:

We study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general symbols and compactness of bounded operators on the Bergman spaces with constant exponents can readily be extended to the variable exponent setting. In particular, if is a finite sum of finite products of Toeplitz operators with symbols from class , then is compact if and only if the Berezin transform of vanishes on the boundary of the unit disc.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1417989

DOI: 10.1155/2018/1417989

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