Fourier-Bessel transforms and generalized uniform Lipschitz classes

Let nu > -1/2, d mu(nu) is defined on R+ = [0,+infinity) by d mu(nu) (x) = [2(nu) Gamma(nu + 1)](-1)x2(nu+1) dx. For f integrable on R+ with respect to d mu(nu) (x) together with its Fourier-Bessel transform of order nu we give necessary and sufficient conditions to belong to the generalized Lipschitz classes H-nu(omega,m) and h(nu)(omega,m). Also a condition for generalized Bessel differentiability of a function is proved.

Automated summary

d mu(nu) is defined on R+ by a specific formula, and necessary conditions for belonging to generalized Lipschitz classes are given. A condition for generalized Bessel differentiability of a function is also proved in the article.