Theorems of Hausdorff-Young and Paley-Wiener type for Fourier transforms of rapidly decreasing functions (Q343297)

Hausdorff-Young and Paley-Wiener type theorems are obtained for the Fourier transforms of the functions of type \((1+| t|)^{\eta}\mu(| t|)e^{-| t| ^{\alpha}\ell(| t|)}\), \(\alpha>1\), where \(\mu\) and \(\ell\) are slowly varying functions. One of the main tools is the Laplace transform for similar functions.