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Off-diagonal estimates for cube skeleton maximal operators

Volume 167 / 2022

Andrea Olivo Colloquium Mathematicum 167 (2022), 187-196 MSC: Primary 42B25; Secondary 43A85. DOI: 10.4064/cm8439-2-2021 Published online: 27 May 2021


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.


  • Andrea OlivoDepartamento de Matemática
    Facultad de Ciencias Exactas y Naturales
    Universidad de Buenos Aires
    Ciudad Universitaria, Pabellón I
    Buenos Aires 1428, Capital Federal, Argentina

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