The finite Hilbert transform acting on $L^{\infty }$

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

The action of the finite Hilbert transform defined on $L^{\infty }(-1,1)$ and taking its values in the Zygmund space $L_{\text{exp}}(-1,1)$ is studied in detail. This is a recip…