m-Berezin Transform and Approximation of Operators on the Bergman Space Over Bounded Symmetric Domains

Agbor, Dieudonne

doi:10.1007/s11785-015-0519-y

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2018

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“…The behaviour of these operators on the Hardy spaces, Bergman spaces, and Fock spaces has been studied widely and a lot of results are available in the literature. The characterization of compactness has been studied in [2][3][4][5][6][7][8] just to cite a few. Given Ω ⊂ R , a measurable function : Ω → [1, ∞) will be called a variable exponent.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Agbor

2018

International Journal of Mathematics and Mathematical Sciences

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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 1 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.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Agbor

2018

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

m-Berezin Transform and Approximation of Operators on the Bergman Space Over Bounded Symmetric Domains

Cited by 1 publication

References 17 publications

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

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

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