Duality and approximation of Bergman spaces

D. Chakrabarti; L. D. Edholm; J. D. McNeal

doi:10.1016/j.aim.2018.10.041

Duality and approximation of Bergman spaces

D. Chakrabarti, L. D. Edholm, J. D. McNeal

Mathematics

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

13 Scopus citations

Abstract

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in Cⁿ, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.

Original language	English
Pages (from-to)	616-656
Number of pages	41
Journal	Advances in Mathematics
Volume	341
DOIs	https://doi.org/10.1016/j.aim.2018.10.041
State	Published - Jan 7 2019

Keywords

Analytic breakdowns
Approximation
Bergman spaces
Duality
Lattice point diagram
Norm convergence

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10.1016/j.aim.2018.10.041

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abstract = "Expected duality and approximation properties are shown to fail on Bergman spaces of domains in Cn, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.",

keywords = "Analytic breakdowns, Approximation, Bergman spaces, Duality, Lattice point diagram, Norm convergence",

author = "D. Chakrabarti and Edholm, {L. D.} and McNeal, {J. D.}",

note = "Funding Information: Research of the first author was supported by a National Science Foundation grant (# 1600371) and by a collaboration grant from the Simons Foundation (# 316632). Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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AU - Chakrabarti, D.

AU - Edholm, L. D.

AU - McNeal, J. D.

N1 - Funding Information: Research of the first author was supported by a National Science Foundation grant (# 1600371) and by a collaboration grant from the Simons Foundation (# 316632). Publisher Copyright: © 2018 Elsevier Inc.

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N2 - Expected duality and approximation properties are shown to fail on Bergman spaces of domains in Cn, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.

AB - Expected duality and approximation properties are shown to fail on Bergman spaces of domains in Cn, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.

KW - Analytic breakdowns

KW - Approximation

KW - Bergman spaces

KW - Duality

KW - Lattice point diagram

KW - Norm convergence

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SN - 0001-8708

VL - 341

SP - 616

EP - 656

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Duality and approximation of Bergman spaces

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Keywords

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