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arXiv · 1911.03006

Sparse bounds for discrete singular Radon transforms

Theresa C. Anderson·Bingyang Hu·Joris Roos
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Abstract

We show that discrete singular Radon transforms along a certain class of polynomial mappings $P:\mathbb{Z}^d\to \mathbb{Z}^n$ satisfy sparse bounds. For $n=d=1$ we can handle all polynomials. In higher dimensions, we pose restrictions on the admissible polynomial mappings stemming from a combination of interacting geometric, analytic and number-theoretic obstacles.

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Theresa C. Anderson, Bingyang Hu, Joris Roos. 2019-11-08. Sparse bounds for discrete singular Radon transforms. https://doi.org/10.4064/cm8296-8-2020

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