The Fourier transform in weighted rearrangement invariant spaces
| Autor: | Mastyło, Mieczysław, Sinnamon, Gord |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society, 152(2024), 1099-1107 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/proc/16610 |
| Popis: | It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it is bounded from $L^p$ to $L^q$, each modified by the same weight, then the weight is bounded above and below and $1\le p=q'\le 2$. Applications prove the non-boundedness on these spaces of an operator related to the Schr\"odinger equation. Comment: 9 pages, no figures |
| Databáze: | arXiv |
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