Spherical maximal operators with fractal sets of dilations on radial functions
| Autor: | Beltran, David, Roos, Joris, Seeger, Andreas |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a given set of dilations $E\subset [1,2]$, Lebesgue space mapping properties of the spherical maximal operator with dilations restricted to $E$ are studied when acting on radial functions. In higher dimensions, the type set only depends on the upper Minkowski dimension of $E$, and in this case complete endpoint results are obtained. In two dimensions we determine the closure of the $L^p\to L^q$ type set for every given set $E$ in terms of a dimensional spectrum closely related to the upper Assouad spectrum of $E$. Comment: 28 pages; 2 figures |
| Databáze: | arXiv |
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