Speaker
Sergey Platonov
(Petrozavovsk State University)
Description
Let a function $f$ belongs to the Lebesgue class $L_p({\mathbb R})$, $1\le p\le 2$, and let $\widehat{f}$ be the Fourier transform of $f$. The classical theorem of E.Titchmarsh states that if the function $f$ belongs to the Lipschitz class $Lip(r,p; {\mathbb R})$, $0 < r\le 1$, then $\hat f$ belongs to the Lebesgue classes $L_q({\mathbb R})$ for $\frac{p}{r p+p-1}< q\le \frac{p}{p-1}$. Using the methods of Fourier-Bessel harmonic analysis we prove an analogue of this result for the the Hankel transform of functions from Nikol'skii type function classes on the half-line $[0,+\infty)$.
Primary author
Sergey Platonov
(Petrozavovsk State University)
