We prove \(\ell ^p\)-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of p in all dimensions \(n\ge 2\).

中文翻译：

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Sharp $$ \ ell ^ p $$ℓp-改进离散抛物面的估计

我们证明了\（\ ell ^ p \）-改进了在所有维度\（n \ ge 2 \）中p的尖锐范围内沿着离散抛物面的平均算子的估计。