Open AccessAbsolute convergence of Fourier integrals and Lipschitz classes
Author(s) -
B.I. Peleshenko
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241115
Subject(s) - lipschitz continuity , omega , fourier transform , mathematics , convergence (economics) , fourier series , pure mathematics , absolute convergence , fourier analysis , mathematical analysis , combinatorics , physics , quantum mechanics , economics , economic growth
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 $H^{\omega}(\mathbb{R})$ and $h^{\omega}(\mathbb{R})$.