Mapping Properties of Fourier Transforms, Revisited

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI:10.1007/s10114-025-3532-8

Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel

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引用次数: 0

Abstract

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces B ^s_p (ℝⁿ) = B ^s_p,p (ℝⁿ), 1 ≤ p ≤ ∞, and between Sobolev spaces H ^s_p (ℝⁿ), 1 < p < ∞. In contrast to the paper 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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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.