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?

12 February 2016 1 6K Report

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?

Hans G. Feichtinger

I am sure there is, but cannot answer it "offhand", hgfei

It should be equivalent to the non-existence of some inequalities

(you cannot control the Wiener amalgam norm by the sum of the L1 norm

of f plus the L1-norm of f^). hgfei

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