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arXiv · 2310.13567

Mapping properties of Fourier transforms, revisited

Dorothee D. Haroske·Leszek Skrzypczak·Hans Triebel
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Abstract

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces $B^s_p(\mathbb{R}^n) = B^s_{p,p}(\mathbb{R}^n)$, $1\le p \le \infty$, and between Sobolev spaces $H^s_p(\mathbb{R}^n)$, $1<p< \infty$. In contrast to the paper {\em H. Triebel, Mapping properties of Fourier transforms. Z. Anal. Anwend. 41 (2022), 133--152}, based mainly on embeddings between related weighted spaces, we rely on wavelet expansions, duality and interpolation of corresponding (unweighted) spaces, and (appropriately extended) Hausdorff-Young inequalities. The degree of compactness will be measured in terms of entropy numbers and approximation numbers, now using the symbiotic relationship to weighted spaces.

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Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel. 2023-10-20. Mapping properties of Fourier transforms, revisited. https://arxiv.org/abs/2310.13567

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