Absolute convergence of Fourier integrals and Lipschitz classes defined with differences of fractional order

Abstract

The necessary and sufficient conditions in terms of Fourier transforms $$$\hat{f}$$$ of functions $$$f\in L^1(\mathbb{R})$$$ are obtained for $$$f$$$ to belong to the Lipschitz classes $$$H_C^{\omega, \alpha}(\mathbb{R})$$$ and $$$h_C^{\omega, \alpha}(\mathbb{R})$$$, defined by differences of fractional order.