2017
Том 69
№ 6

All Issues

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

Golubov B. I., Volosivets S. S.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 693-710.

Citation Example: Golubov B. I., Volosivets S. S. Fourier cosine and sine transforms and generalized Lipschitz classes in uniform metric // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 616-627.

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