Let $(X,{𝒜},\mu )$ be a probability space, let $T$ be a contraction on $L^p(\mu )$ and let $f$ in $L^p(\mu )$, ($p>1$). In this paper, we provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the limit of the weighted ergodic average is ${lim}_{N\to \infty }\frac{1}{A_N}{\sum }_{k=0}^{N-1}{w}_k{T}^{u_k}(f)=0$$\mu$-a.e. We also give applications which concretely prove the effectiveness of the obtained theorems. More precisely, we construct sequences $(w_k)$ and $(u_k)$ that were difficult to deal with previously, which satisfy the conditions of our theorems.

中文翻译：

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关于加权振荡遍历平均数的收敛率

让$(X,{𝒜},\mu )$是一个概率空间，让$吨$收缩${\mathrm{大号}}^p(\mu )$然后让$F$在${\mathrm{大号}}^p(\mu )$, ($p>\mathrm{1个}$). 在本文中，我们提供了适合序列的条件$(w_k)$,$({你}_k)$和$(A_k)$加权遍历平均的极限是${林}_{否\to \infty }\frac{\mathrm{1个}}{A_{否}}{\sum }_{k=0}^{否-\mathrm{1个}}{w}_k{吨}^{{你}_k}(F)=0$$\mu$-ae 我们还给出了应用程序，具体证明了所获得定理的有效性。更准确地说，我们构造序列$(w_k)$和$({你}_k)$以前很难处理的，满足我们定理的条件。