Bounds for discrete multilinear spherical maximal functions in higher dimensions
| Autor: | Anderson, Theresa C., Palsson, Eyvindur Ari |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms.12465 |
| Popis: | We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions $d \geq 5$. That is, we show that this operator is bounded on $l^{p}(\mathbb{Z}^d)\times l^{q}(\mathbb{Z}^d) \to l^{r}(\mathbb{Z}^d)$ for $\frac{1}{p} + \frac{1}{q} \geq \frac{1}{r}$ and $r>\frac{d}{2d-2}$ and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions $d=3,4$, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree $k$, $\ell$-linear operators. Comment: References updated, typo corrected |
| Databáze: | arXiv |
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