Open AccessOn convergence of Fourier integrals and Lipschitz spaces defined with differences of fractional order
Author(s) -
B.I. Peleshenko,
T.N. Semirenko
Publication year - 2015
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241509
Subject(s) - lipschitz continuity , mathematics , order (exchange) , convergence (economics) , fourier transform , fractional calculus , fourier series , mathematical analysis , pure mathematics , economics , finance , 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 $H^{\omega}(\mathbb{R})$, $h^{\omega}(\mathbb{R})$.