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arXiv · 1405.5566

Discrete maximal functions in higher dimensions and applications to ergodic theory

Mariusz Mirek·Bartosz Trojan
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Abstract

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1 \max\{p, p/(p-1)\}$. Moreover, we obtain the estimates which are uniform in the coefficients of a polynomial mapping of fixed degree.

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Mariusz Mirek, Bartosz Trojan. 2014-05-21. Discrete maximal functions in higher dimensions and applications to ergodic theory. https://arxiv.org/abs/1405.5566

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