论文标题
在更高的codimension表面上的离散最大运算符
Discrete maximal operators over surfaces of higher codimension
论文作者
论文摘要
与较高的曲折的曲流相结合，并分别是连续运算符的离散变体，在谐波分析，离散的几何形状和分析数理论研究中是两个重要但单独的主题。在这里，我们将这些主题团结起来，研究涉及较高（中级）编成二维整合的运算符的离散类似物。我们考虑了一个最大运算符，该操作员平均进行三角形配置，并证明几个接近最佳的界限。我们方法的一个独特特征是使用多线性通过一个相当笼统的想法来获得非平凡的$ \ ell^1 $估算，该想法可能适用于其他问题。
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research. Here we unite these themes to study discrete analogues of operators involving higher (intermediate) codimensional integration. We consider a maximal operator that averages over triangular configurations and prove several bounds that are close to optimal. A distinct feature of our approach is the use of multilinearity to obtain nontrivial $\ell^1$-estimates by a rather general idea that is likely to be applicable to other problems.
