Carleson Measures for Variable Exponent Bergman Spaces

Chacón, Gerardo; Rafeiro, Humberto; Vallejo, Juan Camilo

doi:10.1007/s11785-016-0573-0

Cited by 12 publications

(11 citation statements)

References 22 publications

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“…There it was shown, amongst other things, that the Bergman projector is bounded from (⋅) onto (⋅) . Also in [10], the authors studied Carleson measures in such spaces.…”

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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“…There it was shown, amongst other things, that the Bergman projector is bounded from (⋅) onto (⋅) . Also in [10], the authors studied Carleson measures in such spaces.…”

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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show abstract

“…In this section, we show an example of a variable log −Hölder continuous exponent p(·) for which H p(·) (D) differs from all classical spaces H p (D). Define p : [0, 2π] → [2,3] as…”

Section: An Examplementioning

confidence: 99%

“…For example, in [9] a version of BM O spaces with variable exponents is considered. Bergman spaces with variable exponents have been studied in [1,2,3] and a different approach has been taken in [10] and [11], much of the research done in the area assume the log-Hölder condition on the exponent, which is a growth condition that usually guarantees the boundedness of a Hardy-Littlewood maximal operator in a related space. One case of function spaces on unbounded domains have been studied in [18].…”

Section: Introductionmentioning

confidence: 99%