New estimates for the minimal L2 solution of ∂ and applications to geometric function theory in weighted Bergman spaces

Alexander P. Schuster; Dror Varolin

doi:10.1515/crelle-2012-0072

New estimates for the minimal L² solution of ∂ and applications to geometric function theory in weighted Bergman spaces

Alexander P. Schuster
, Dror Varolin

Mathematics

San Francisco State University
American University in Cairo

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We introduce new twisting techniques to establish new estimates for the minimal L² solution of ∂ on weighted Bergman spaces in the unit ball. The estimate is used to obtain off-diagonal decay bounds for the associated Bergman kernel, and also improve sup-norm estimates obtained some time ago by Berndtsson.

Original language	English
Pages (from-to)	173-201
Number of pages	29
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	691
DOIs	https://doi.org/10.1515/crelle-2012-0072
State	Published - Jun 1 2014

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abstract = "We introduce new twisting techniques to establish new estimates for the minimal L2 solution of ∂ on weighted Bergman spaces in the unit ball. The estimate is used to obtain off-diagonal decay bounds for the associated Bergman kernel, and also improve sup-norm estimates obtained some time ago by Berndtsson.",

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AU - Varolin, Dror

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N2 - We introduce new twisting techniques to establish new estimates for the minimal L2 solution of ∂ on weighted Bergman spaces in the unit ball. The estimate is used to obtain off-diagonal decay bounds for the associated Bergman kernel, and also improve sup-norm estimates obtained some time ago by Berndtsson.

AB - We introduce new twisting techniques to establish new estimates for the minimal L2 solution of ∂ on weighted Bergman spaces in the unit ball. The estimate is used to obtain off-diagonal decay bounds for the associated Bergman kernel, and also improve sup-norm estimates obtained some time ago by Berndtsson.

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DO - 10.1515/crelle-2012-0072

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JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

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New estimates for the minimal L² solution of ∂ and applications to geometric function theory in weighted Bergman spaces

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