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

  • B. I. Golubov Moscow Inst. Phys. and Technol. (State Univ.), Russia
  • S. S. Volosivets Saratov State Univ., Russia

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.
Published
25.05.2012
How to Cite
GolubovB. I., and VolosivetsS. S. “Fourier Cosine and Sine Transforms and Generalized Lipschitz Classes in Uniform Metric”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 616-27, http://umj.imath.kiev.ua/index.php/umj/article/view/2602.
Section
Research articles