Sobolev regularity of the ∂̄-equation on the Hartogs triangle

Debraj Chakrabarti, Mei Chi Shaw

Research output: Contribution to journalArticlepeer-review

12 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 languageEnglish
Pages (from-to)241-258
Number of pages18
JournalMathematische Annalen
Volume356
Issue number1
DOIs
StatePublished - May 2013

Keywords

  • 32A07
  • 32W05

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