Concerning one Paley-Wiener theorem

00:00 05-01-2011
<p style="TEXT-ALIGN: left; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" class="MsoNormal"><font face="Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: 'Arial', 'sans-serif'; COLOR: black; FONT-SIZE: 14px">In a joint work with S. Tikhonov, we prove weighted analogues of the Paley-Wiener theorem on integrability of the Hilbert transform of an integrable odd function which is monotone on $mathbb{R}_+$. This extends Hardy-Littlewood's and Flett's results to the case $p=1$ under the assumption of (general) monotonicity for an even/odd function.<br />Further, relations between the Fourier transform and Hilbert transform will be discussed.</span><span style="FONT-FAMILY: 'Arial', 'sans-serif'; COLOR: black"><font size="2"> </font></span><span style="COLOR: black"></span></font></p>