Discrete maximal functions in higher dimensions and applications to ergodic theory

By Mariusz Mirek, Bartosz Trojan. 2014

49 citations recorded by the source corpus.

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 $1<p<\infty$ and $r>\max\{p, p/(p-1)\}$. Moreover, we obtain the estimates which are uniform in the coefficients of a polynomial mapping of fixed degree.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2fc1468d17bdd34b2153300398b1dbfe2c7e3070

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In Applied Mathematics

1. Mariusz Mirek
2. E. Stein
3. Bartosz Trojan
4. Yongsheng Han
5. Dachun Yang
6. G. Lu
7. Jean Van Schaftingen
8. Victor Lie

In Mathematical Physics

1. Mariusz Mirek
2. E. Stein
3. Bartosz Trojan
4. Yongsheng Han
5. Dachun Yang
6. Victor Lie

Citations in the corpus

• L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates (2015, background): “Variational estimates have been the subject of many papers, see [9, 10, 11, 16, 22] and the references therein.”