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Bibliographic Details
Main Authors:	Carro, María J., Naibo, Virginia, Soria-Carro, María
Format:	Preprint
Published:	2024
Subjects:	Functional Analysis Classical Analysis and ODEs 42B20
Online Access:	https://arxiv.org/abs/2405.02725
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Table of Contents:

We prove Hilbert transform identities involving conformal maps via the use of Rellich identity and the solution of the Neumann problem in a graph Lipschitz domain in the plane. We obtain as consequences new $L^2$-weighted estimates for the Hilbert transform, including a sharp bound for its norm as a bounded operator in weighted $L^2$ in terms of a weight constant associated to the Helson-Szegö theorem.