Fourier cosine and sine transforms and generalized Lipschitz classes in uniform metric

• Date: 2012
• Main Authors: Golubov, B. I., Volosivets, S. S., Голубов, Б. І., Волосівец, С. С.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2602
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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^{\ome...