Carro Rossell, María JesúsNaibo, VirginiaSoria Carro, María2026-01-142026-01-1420240022-1236https://hdl.handle.net/20.500.14352/130243We 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 weighted estimates for the Hilbert transform, including a sharp bound for its norm as a bounded operator in weighted in terms of a weight constant associated to the Helson-Szegö theorem.engjournal articlehttps://doi.org/10.1016/j.jfa.2023.110271open accessHilbert transformRellich identityA2-conjectureHelson–Szegö theoremMatemáticas (Matemáticas)12 Matemáticas