New York Journal of Mathematics
Volume 20 (2014) 627-643


Željko Čučković and Sönmez Şahutoğlu

Compactness of products of Hankel operators on convex Reinhardt domains in C2

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Published: June 21, 2014
Keywords: Hankel operators, analytic disks, Reinhardt domains
Subject: Primary 47B35; Secondary 32A07

Let Ω be a piecewise smooth bounded convex Reinhardt domain in C2. Assume that the symbols ϕ and ψ are continuous on \barΩ and harmonic on the disks in the boundary of Ω. We show that if the product of Hankel operators H*ψ Hϕ is compact on the Bergman space of Ω, then on any disk in the boundary of Ω, either ϕ or ψ is holomorphic.

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University of Toledo, Department of Mathematics & Statistics, Toledo, OH 43606, USA