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

TL;DR

This paper provides estimates for the essential norm of Hankel operators on convex domains in complex two-dimensional space, linking these estimates to boundary behavior of the symbol function.

Contribution

It introduces new boundary-based estimates for Hankel operator norms on convex domains in a7^2, focusing on the role of f4 derivatives along boundary disks.

Findings

Essential norm bounds depend on boundary f4 derivatives.

Estimates are valid for convex domains with smooth boundary.

Results connect boundary harmonicity to operator norms.

Abstract

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