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arXiv · 2011.02656

A Sufficient condition for compactness of Hankel operators

Mehmet Celik·Sonmez Sahutoglu·Emil J. Straube
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Abstract

Let $Ω$ be a bounded convex domain in $\mathbb{C}^{n}$. We show that if $φ\in C^{1}(\overlineΩ)$ is holomorphic along analytic varieties in $bΩ$, then $H^{q}_φ$, the Hankel operator with symbol $φ$, 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).

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Mehmet Celik, Sonmez Sahutoglu, Emil J. Straube. 2021-07-08. A Sufficient condition for compactness of Hankel operators. https://doi.org/10.7900/jot.2021apr04.2334

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