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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F71226401%3A_____%2F25%3AN0101127" target="_blank" >RIV/71226401:_____/25:N0101127 - isvavai.cz</a>
Alternative codes found
RIV/60460709:41310/25:102981
Result on the web
<a href="https://link.springer.com/article/10.1007/s00041-025-10206-2" target="_blank" >https://link.springer.com/article/10.1007/s00041-025-10206-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00041-025-10206-2" target="_blank" >10.1007/s00041-025-10206-2</a>

Result language
angličtina
Original language name
Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces
Original language description
We establish that the Fourier transform $F: L^p(R^d)to L^{p',p}(R^d)$, for $din N$ and $1<p<2$, is not strictly singular, thereby confirming the optimality of the source and target spaces. A similar result is obtained for Fourier series on $L^p(T^d)$, with sequence Lorentz spaces as the target. These findings complement known results, which state that $F: L^p(R^d)to L^{p'}(R^d)$ is finitely strictly singular and then also strictly singular, and provide further insight into the degrees of non-compactness of $F.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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