Endpoint sparse domination for classes of multiplier transformations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913345103200256 |
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| author | Beltran, David Roos, Joris Seeger, Andreas |
| author_facet | Beltran, David Roos, Joris Seeger, Andreas |
| contents | We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipliers based on natural localized $M^{p\to q}$ norms which express appropriate endpoint regularity hypotheses. The applications include new and optimal sparse bounds for classical oscillatory multipliers and multi-scale versions of radial bump multipliers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12437 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Endpoint sparse domination for classes of multiplier transformations Beltran, David Roos, Joris Seeger, Andreas Classical Analysis and ODEs 42B15, 42B20, 42B25 We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipliers based on natural localized $M^{p\to q}$ norms which express appropriate endpoint regularity hypotheses. The applications include new and optimal sparse bounds for classical oscillatory multipliers and multi-scale versions of radial bump multipliers. |
| title | Endpoint sparse domination for classes of multiplier transformations |
| topic | Classical Analysis and ODEs 42B15, 42B20, 42B25 |
| url | https://arxiv.org/abs/2212.12437 |