Relations between the Fourier and the Hilbert transform

In this talk we discuss various conditions of the

integrability of the Fourier transform of a function of bounded

variation and their connections to the behavior of the Hilbert

transform of a related function. Correspondingly, the considered

spaces of functions with integrable Fourier transform are intimately

related with the real Hardy space. One of the most important

connections for the two transforms is given by the space introduced

(for different purposes) by Johnson and Warner.