2019
Том 71
№ 4

# Volosivets S. S.

Articles: 1
Article (English)

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

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 616-627

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.