Sobolev regularity of the ∂̄-equation on the Hartogs triangle

Debraj Chakrabarti; Mei Chi Shaw

doi:10.1007/s00208-012-0840-y

Sobolev regularity of the ∂̄-equation on the Hartogs triangle

Debraj Chakrabarti, Mei Chi Shaw

Mathematics

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13 Scopus citations

Abstract

The regularity of the ∂̄-problem on the domain {{pipe}z₁{pipe} < {pipe}z₂{pipe} < 1} in ℂ₂ is studied using L₂-methods. Estimates are obtained for the canonical solution in weighted L₂-Sobolev spaces with a weight that is singular at the point (0, 0). In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.

Original language	English
Pages (from-to)	241-258
Number of pages	18
Journal	Mathematische Annalen
Volume	356
Issue number	1
DOIs	https://doi.org/10.1007/s00208-012-0840-y
State	Published - May 2013

Keywords

32A07
32W05

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title = "Sobolev regularity of the {\=∂}-equation on the Hartogs triangle",

abstract = "The regularity of the {\=∂}-problem on the domain {{pipe}z1{pipe} < {pipe}z2{pipe} < 1} in ℂ2 is studied using L2-methods. Estimates are obtained for the canonical solution in weighted L2-Sobolev spaces with a weight that is singular at the point (0, 0). In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.",

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author = "Debraj Chakrabarti and Shaw, {Mei Chi}",

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AU - Chakrabarti, Debraj

AU - Shaw, Mei Chi

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PY - 2013/5

Y1 - 2013/5

N2 - The regularity of the ∂̄-problem on the domain {{pipe}z1{pipe} < {pipe}z2{pipe} < 1} in ℂ2 is studied using L2-methods. Estimates are obtained for the canonical solution in weighted L2-Sobolev spaces with a weight that is singular at the point (0, 0). In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.

AB - The regularity of the ∂̄-problem on the domain {{pipe}z1{pipe} < {pipe}z2{pipe} < 1} in ℂ2 is studied using L2-methods. Estimates are obtained for the canonical solution in weighted L2-Sobolev spaces with a weight that is singular at the point (0, 0). In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.

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JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1

ER -

Sobolev regularity of the ∂̄-equation on the Hartogs triangle

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