Cauchy-type integrals in several complex variables

Loredana Lanzani, Elias M. Stein

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We present the theory of Cauchy–Fantappié integral operators, with emphasis on the situation when the domain of integration, D, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter z ∈ D. The goal is to prove Lp estimates for these operators and, as a consequence, to obtain Lp estimates for the canonical Cauchy–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type).

Original languageEnglish (US)
Pages (from-to)241-285
Number of pages45
JournalBulletin of Mathematical Sciences
Volume3
Issue number2
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

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Cauchy-type Integral
Several Complex Variables
Lp Estimates
Bergman Projection
Boundary Regularity
Cauchy Integral
Projection Operator
Operator
Integral Operator
Analytic function
kernel

Keywords

  • 31B
  • 32A36
  • 32A50
  • 42B

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cauchy-type integrals in several complex variables. / Lanzani, Loredana; Stein, Elias M.

In: Bulletin of Mathematical Sciences, Vol. 3, No. 2, 01.01.2013, p. 241-285.

Research output: Contribution to journalArticle

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