Essential norm estimates for Hankel operators on convex domains in ${\mathbb{C}}^2$

Abstract

Let $\Omega \subset {\mathbb{C}}^2$ be a bounded convex domain with $C^1$-smooth boundary and $\phi \in C^1(\overline{\Omega })$ such that $\phi$ is harmonic on the nontrivial disks in the boundary. We estimate the essential norm of the Hankel operator $H_{\phi }$ in terms of the $\overline{\partial }$ derivatives of $\phi$ "along" the nontrivial disks in the boundary.

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References in corpus (1)

• Compactness of Hankel operators and analytic discs in the boundary of pseudoconvex domains