On asymptotic and essential Toeplitz and Hankel integral operator

C. Bellavita; G. Stylogiannis

On asymptotic and essential Toeplitz and Hankel integral operator

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arxiv 2409.10014 v1 pith:QJFZZM7T submitted 2024-09-16 math.FA math.CVmath.OA

C. Bellavita , G. Stylogiannis This is my paper · ORCID

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abstract

In this article we consider the generalized integral operators acting on the Hilbert space $H^2$. We characterize when these operators are uniform, strong and weakly asymptotic Toeplitz and Hankel operators. Moreover we completely describe the symbols $g$ for which these operators are essentially Hankel and essentially Toeplitz.

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For BMOA symbols g1 and g2, the meromorphic optimal domains (T_{g1},H^p) and (T_{g2},H^p) coincide exactly when each symbol is the other symbol integrated against a bounded analytic function, with the two functions re...

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