Discrete maximal functions in higher dimensions and applications to ergodic theory
Discrete maximal functions in higher dimensions and applications to ergodic theory
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DOI：
10.1353/ajm.2016.0045
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发表时间：
2014-05
影响因子：
1.7
通讯作者：
Mariusz Mirek;B. Trojan
中科院分区：
文献类型：
--
作者：
Mariusz Mirek;B. Trojan
我们建立了一个高维对应的Bourgain的逐点遍历定理沿着任意整数值多项式映射。我们通过证明在L^p空间上对所有1\max\{p，p/（p-1）\}的变分估计V_r来实现这一点。此外，我们还得到了固定次数多项式映射系数的一致估计。
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.