The cauchy transform on bounded domains

J. M. Anderson, A. Hinkkanen

Research output: Contribution to journalArticlepeer-review


Suppose that ƒ is in L2(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ2 ≤ (2/α)ƖƖƒƖƖ2, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.

Original languageEnglish (US)
Pages (from-to)179-185
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Sep 1989
Externally publishedYes


  • Link homotopy
  • Links
  • Whitney trick

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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