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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Communicated by Ronald A. DeVore.
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Arazy, J., Fisher, S.D. & Peetre, J. Hankel operators on planar domains. Constr. Approx 6, 113–138 (1990). https://doi.org/10.1007/BF01889353
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DOI: https://doi.org/10.1007/BF01889353