论文标题
离散曲线的$ \ ell^p $改进问题的一些亚临界估计值
Some subcritical estimates for the $\ell^p$-improving problem for discrete curves
论文作者
论文摘要
我们将基督的改进方法应用于离散的$ \ ell^p $ - 提示问题，用于$ \ mathbb {z}^d $中的多项式曲线，沿多项式曲线沿多项式曲线沿多项式曲线。结合某些对某些Diophantine方程的解决方案的解决方案数量的基本估计，我们获得了亚临界体制中的平均$ \ Mathcal {a} _n $的p'p'$估计值的限制性弱型$ p \。此处获得的$ n $的依赖性很清晰，除了$ε$ -loss。
We apply Christ's method of refinements to the $\ell^p$-improving problem for discrete averages $\mathcal{A}_N$ along polynomial curves in $\mathbb{Z}^d$. Combined with certain elementary estimates for the number of solutions to certain special systems of diophantine equations, we obtain some restricted weak-type $p \to p'$ estimates for the averages $\mathcal{A}_N$ in the subcritical regime. The dependence on $N$ of the constants here obtained is sharp, except maybe for an $ε$-loss.
