Compact Hankel operators on generalized Bergman spaces of the polydisc

Details Compact Hankel operators on generalized Bergman spaces of the polydisc Compact Hankel operators on generalized Bergman spaces of the polydisc

2010-04-07

arxiv.org/abs/1004.1152v1

Mathematics

Functional Analysis

13 pages, to appear in Integral Equation and Operator Theory

Scientific paper

We show that for $f$ a continuous function on the closed polydisc
$\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on
the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition
$f=h+g$, where $h$ is in the ball algebra and $g$ vanishes on the boundary of
the polydisc.

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