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Discrete Double Hilbert Transforms Along Polynomial Surfaces
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Paper
Discrete Double Hilbert Transforms Along Polynomial Surfaces
2025
Overview
We obtain a necessary and sufficient condition on a polynomial \\(P(t_1,t_2)\\) for the \\(\\ell^{p}\\) boundedness of the discrete double Hilbert transforms associated with \\(P(t)\\) for \\(1 < p < \\infty\\). The proof is based on the multi-parameter circle method treating the cases of \\(|t_1|\\not\\approx |t_2|\\) arising from \\(1/t_1\\) and \\(1/t_2\\).
Publisher
Cornell University Library, arXiv.org
Subject
