TY - JOUR AU - B. I. Golubov AU - S. S. Volosivets PY - 2012/05/25 Y2 - 2024/03/29 TI - Fourier cosine and sine transforms and generalized Lipschitz classes in uniform metric JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 5 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2602 AB - For functions $f \in L^1(\mathbb{R}_{+})$ with cosine (sine) Fourier transforms $\widehat{f}_c(\widehat{f}_s)$ in $L^1(\mathbb{R})$, we give necessary and sufficient conditions in terms of $\widehat{f}_c(\widehat{f}_s)$ for $f$ to belong to generalized Lipschitz classes $H^{\omega, m}$ and $h^{\omega, m}$. Conditions for the uniform convergence of the Fourier integral and for the existence of the Schwartz derivative are also obtained. ER -