Spherical maximal operators with fractal sets of dilations on radial functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911472478584832 |
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| author | Beltran, David Roos, Joris Seeger, Andreas |
| author_facet | Beltran, David Roos, Joris Seeger, Andreas |
| contents | 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 $E$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical maximal operators with fractal sets of dilations on radial functions Beltran, David Roos, Joris Seeger, Andreas Classical Analysis and ODEs 42B25, 28A80 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 $E$. |
| title | Spherical maximal operators with fractal sets of dilations on radial functions |
| topic | Classical Analysis and ODEs 42B25, 28A80 |
| url | https://arxiv.org/abs/2412.09390 |