Which Is the f in L^{1}(\mb{R}) with Fourier transorm in L^{1}(\mb{R}), but niether f nor its Fourier transform is in the Wiener's space?

Is there an example for a  function f in L^{1}(\mb{R}) such that  Fourier transform of f is also in  L^{1}(\mb{R}), but neither f nor its Fourier transform is in the Wiener's space?

12 February 2016 6,326 1 View