Discrete Double Hilbert Transforms Along Polynomial Surfaces

2022/09/16 by Kim, Joonil, Song, Hoyoung
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.08072

Abstract

We obtain a necessary and sufficient condition on a polynomial P(t₁,t₂) for the ℓ^p boundedness of the discrete double Hilbert transforms associated with P(t) for 1 < p < ∞. The proof is based on the multi-parameter circle method treating the cases of |t₁|\not≈ |t₂| arising from 1/t₁ and 1/t₂.

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