6 papers · 1 filter
Simplex Averaging Operators: Quasi-Banach and -Improving Bounds in Lower Dimensions
Alex Iosevich, Eyvindur Ari Palsson, Sean R. Sovine
We establish some new -improving bounds for the -simplex averaging operators that hold in dimensions . As a consequence of these -improving bounds we o…
Supercritical discrete restriction estimates for forms in many variables
Brian Cook, Kevin Hughes, Eyvindur Palsson
We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmet…
Bounds for discrete multilinear spherical maximal functions in higher dimensions
Theresa C. Anderson, Eyvindur Ari Palsson
We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions . That is, we show that this operator is bounded on $l^{p}(\mat…
Bounds for discrete multilinear spherical maximal functions
Theresa C. Anderson, Eyvindur Ari Palsson
We define a discrete version of the bilinear spherical maximal function, and show bilinear bounds for $d \ge…
An improved dimensional threshold for the angle problem
Alex Iosevich, Eyvindur A. Palsson
The Falconer distinct distance problem asks for a compact set how large its Hausdorff dimension needs to be to ensure that the Lebesgue measure of its distan…
Variation-norm and fluctuation estimates for ergodic bilinear averages
Yen Do, Richard Oberlin, Eyvindur A. Palsson
For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It foll…