Dimension-Free L2 Maximal Inequality for Spherical Means in the Hypercube
Dimension-Free L2 Maximal Inequality for Spherical Means in the Hypercube
复制标题
超立方体球均值的无量纲L2最大不等式
作者：
A. Harrow;A. Kolla;L. Schulman
我们建立了标题中所声称的最大不等式。在组合术语中，这意味着对于足够小的e>；0，对于所有n，对n维超立方体的顶点的e部分的任何标记必然留下顶点x，使得所标记的顶点是以x为中心的每个球体的少数。
We establish the maximal inequality claimed in the title. In combinatorial terms this has the implication that for sufficiently small e > 0, for all n, any marking of an e fraction of the vertices of the n-dimensional hypercube necessarily leaves a vertex x such that marked vertices are a minority of every sphere centered at x.