Kahane–Katznelson–de Leeuw theorem and absolute convergence of Fourier series
We extend the Kahane-Katznelson-de Leeuw theorem to smoothness spaces by showing that for any g is an element of W-l,W-2(T-d), there exists a function f is an element of C-l (T-d) satisfying |f (<^>)(n)|>=|g(<^>)(n)| and omega r(D-l f,t)(infinity )approximate to omega(r)(D-l g,t)(2),...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/489164 |
| Acceso en línea: | http://hdl.handle.net/2072/489164 |
| Access Level: | acceso embargado |
| Palabra clave: | Kahane–Katznelson–de Leeuw theorem smoothness 51 |
| Sumario: | We extend the Kahane-Katznelson-de Leeuw theorem to smoothness spaces by showing that for any g is an element of W-l,W-2(T-d), there exists a function f is an element of C-l (T-d) satisfying |f (<^>)(n)|>=|g(<^>)(n)| and omega r(D-l f,t)(infinity )approximate to omega(r)(D-l g,t)(2), t > 0. We apply this result to solve the Bernstein problem of finding necessary and sufficient conditions for the absolute convergence of multiple Fourier series. Finally, we explore the absolute integrability of Fourier transforms. |
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