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arXiv · 2212.12437

Endpoint sparse domination for classes of multiplier transformations

David Beltran·Joris Roos·Andreas Seeger
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Abstract

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.

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David Beltran, Joris Roos, Andreas Seeger. 2022-12-23. Endpoint sparse domination for classes of multiplier transformations. https://doi.org/10.1007/s00209-023-03345-z

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