This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform $F$ between some weighted function spaces on $\mathbb{R}^n$.
Mapping properties of Fourier transforms, revisited
Mapping properties of the Fourier transform in spaces with dominating mixed smoothness
On Laplace--Carleson embeddings, and $L^p$-mapping properties of the Fourier transform
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