Hankel operators on planar domains

Jonathan Arazy, Stephen D. Fisher, Jaak Peetre

Research output: Contribution to journalArticlepeer-review


Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves Let A denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and let P denote the orthogonal projection of L2(Ω, dA) onto A. A function b in A induces a Hankel operator (densely defined) on A by the rule Hb(g)=(I-P)bg. This paper continues earlier investigations of the authors and others by determining conditions under which Hb is bounded, compact, or lies in the Schatten-von Neumann ideal Sp, 1<p<∞

Original languageEnglish
Pages (from-to)113-138
Number of pages26
JournalConstructive Approximation
Issue number2
StatePublished - Jun 1990


  • AMS classification: 47B10, 41A35, 46E15
  • Besov space
  • Bloch space
  • Hankel operator
  • Schatten-von Neumann ideal

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


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