The finite Hilbert transform acting in the Zygmund space LlogL

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

The finite Hilbert transform T is a singular integral operator which maps the Zygmund space $LlogL:=LlogL(-1,1)$ continuously into $L^1:=L^1(-1,1)$. By extending the Parseval and P…