Hankel operators on planar domains |
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Authors: | Jonathan Arazy Stephen D Fisher Jaak Peetre |
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Institution: | 1. Department of Mathematics, University of Haifa, 31999, Haifa, Israel 2. Department of Mathematics, Northwestern University, 60208, Evanston, Illinois, USA 3. Department of Mathematics, University of Stockholm, Stockholm, Sweden
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Abstract: | Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves LetA denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and letP denote the orthogonal projection ofL 2(Ω,dA) ontoA. A functionb inA induces a Hankel operator (densely defined) onA by the ruleH b (g)=(I?P)bg. This paper continues earlier investigations of the authors and others by determining conditions under whichH b is bounded, compact, or lies in the Schatten-von Neumann idealS p , 1<p<∞ |
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