Discrete maximal operators and pinned simplices

Abstract

We prove ${\ell }^2$ estimates for certain discrete maximal operators associated to simplices. These operators are generalizations of the discrete spherical maximal operator.

Due to an error in the original version of this paper the combinatorial application no longer included. The paper now focuses soley on what was the main and most important result of the original version. In light of the more general statement of the main result, we have changed the tile by removing the word multilinear