On the Hankel transform of functions from Nikol'skii type classes

Let a function f belong to the Lebesgue class L-p(R), 1 <= p <= 2, and let (f) over cap 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; R), 0 < r <= 1, then <(f)over cap> belongs to the Lebesgue classes L-q(R) for p/rp+p-1 < q <= p/p-1. In this paper 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,+infinity).

Automated summary

This paper proves an analogue of a classical theorem for the Hankel transform of functions from Nikol'skii type function classes on the half-line [0,+infinity).