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- W3102227720 abstract "Consider the discrete cubic Hilbert transform defined on finitely supported functions $f$ on $mathbb{Z}$ by begin{eqnarray*} H_3f(n) = sum_{m not = 0} frac{f(n- m^3)}{m}. end{eqnarray*} We prove that there exists $r <2$ and universal constant $C$ such that for all finitely supported $f,g$ on $mathbb{Z}$ there exists an $(r,r)$-sparse form ${Lambda}_{r,r}$ for which begin{eqnarray*} left| langle H_3f, g rangle right| leq C {Lambda}_{r,r} (f,g). end{eqnarray*} This is the first result of this type concerning discrete harmonic analytic operators. It immediately implies some weighted inequalities, which are also new in this setting." @default.
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- W3102227720 date "2019-01-01" @default.
- W3102227720 modified "2023-10-06" @default.
- W3102227720 title "Sparse bounds for the discrete cubic Hilbert transform" @default.
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- W3102227720 doi "https://doi.org/10.2140/apde.2019.12.1259" @default.
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