Relations between the Fourier and the Hilbert transform

Mon, 21/05/2012 - 14:00
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.