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

Željko Čučković, Sönmez Şahutoğlu

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 non-trivial 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 non-trivial disks in the boundary.


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References


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DOI: http://dx.doi.org/10.7146/math.scand.a-25793

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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