The spectrum of the Leray transform for convex Reinhardt domains in C2

David E. Barrett, Loredana Lanzani

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in C2. Our class is self-dual; it contains some domains with less than C2-smooth boundary and also some domains with smooth boundary and degenerate Levi form. L2-regularity is proved, and essential spectra are computed with respect to a family of boundary measures which includes surface measure. A duality principle is established providing explicit unitary equivalence between operators on domains in our class and operators on the corresponding polar domains. Many of these results are new even for the classical case of smoothly bounded strongly convex Reinhardt domains.

Original languageEnglish (US)
Pages (from-to)2780-2819
Number of pages40
JournalJournal of Functional Analysis
Volume257
Issue number9
DOIs
StatePublished - Nov 1 2009
Externally publishedYes

Keywords

  • Cauchy integral
  • Essential spectrum
  • Kerzman-Stein operator
  • Leray transform
  • Reinhardt domain

ASJC Scopus subject areas

  • Analysis

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