Discrete Double Hilbert Transforms Along Polynomial Surfaces

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...

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Bibliographic Details
Main Authors Kim, Joonil, Song, Hoyoung
Format Journal Article
LanguageEnglish
Published 16.09.2022
Subjects
Mathematics - Classical Analysis and ODEs
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Summary: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 $1/t_2$.
DOI:10.48550/arxiv.2209.08072