Fourier-Bessel transforms and generalized uniform Lipschitz classes

Abstract

Let ν>−1/2, dμν is defined on R+=[0,+∞) by dμν(x)=[2νΓ(ν+1)]−1x2ν+1dx. For f integrable on R+ with respect to dμν(x) together with its Fourier-Bessel transform of order ν we give necessary and sufficient conditions to belong to the generalized Lipschitz classes Hνω,m and hνω,m. Also a condition for generalized Bessel differentiability of a function is proved.

Topics & Concepts