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 $1<p<\infty$ 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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1495-1532
Launched on MUSE
2016-12-09
Open Access
No
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