The cauchy-leray integral: Counterexamples to the Lp-theory

Loredana Lanzani, Elias M. Stein

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We prove the optimality of the hypotheses guaranteeing the Lp-boundedness for the Cauchy-Leray integral in Cn, n ≥ 2, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong C-linear convexity, and the regularity of order 2, are both necessary.

Original languageEnglish (US)
Pages (from-to)1609-1621
Number of pages13
JournalIndiana University Mathematics Journal
Issue number5
StatePublished - 2019


  • Cauchy Integral
  • Cauchy-Leray integral
  • Cauchy-Szego projection
  • Hardy space
  • Lebesgue space
  • Leray-Levi measure
  • Minimal smoothness
  • Pseudoconvex domain

ASJC Scopus subject areas

  • General Mathematics


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