Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces

David E. Edmunds, Petr Gurka, Jan Lang

We establish that the Fourier transform $\mathcal{F}:L^p({\mathbb{R}}^d)\to L^{p^{\prime },p}({\mathbb{R}}^d)$, for $d\in \mathbb{N}$ and $1<p<2$, is not strictly singular, thereby confirming t…