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A Sufficient condition for compactness of Hankel operators (2011.02656v2)
Published 5 Nov 2020 in math.CV and math.FA
Abstract: Let $\Omega$ be a bounded convex domain in $\mathbb{C}{n}$. We show that if $\varphi \in C{1}(\overline{\Omega})$ is holomorphic along analytic varieties in $b\Omega$, then $H{q}_{\varphi}$, the Hankel operator with symbol $\varphi$, is compact. We have shown the converse earlier, so that we obtain a characterization of compactness of these operators in terms of the behavior of the symbol relative to analytic structure in the boundary. A corollary is that Toeplitz operators with these symbols are Fredholm (of index zero).