Simplex Averaging Operators: Quasi-Banach and $L^p$-Improving Bounds in Lower Dimensions

Alex Iosevich, Eyvindur Ari Palsson, Sean R. Sovine

We establish some new $L^p$-improving bounds for the $k$-simplex averaging operators $S^k$ that hold in dimensions $d\ge k$. As a consequence of these $L^p$-improving bounds we o…