Off-diagonal estimates for cube skeleton maximal operators
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 187-196
MSC: Primary 42B25; Secondary 43A85.
DOI: 10.4064/cm8439-2-2021
Published online: 27 May 2021
Abstract
We provide off-diagonal estimates for maximal operators arising from a geometric problem of estimating the size of a certain geometric configuration of $k$-skeletons in $\mathbb {R}^n$. This is achieved by interpolating a weak-type endpoint estimate with the known diagonal bounds. The endpoint estimate is proved by combining a geometric result about $k$-skeletons and adapting an argument used to prove off-diagonal estimates for the circular maximal function in the plane.
