Convergence of weighted ergodic averages

Abstract

Let $(X,\mathcal{A},\mu )$ be a probability space and let $T$ be a contraction on $L^2(\mu )$. We provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the weighted ergodic limit $\underset{N\to \infty }{\lim }\frac{1}{A_N}{\sum }_{k=0}^{N-1}{w}_k{T}^{u_k}(f)=0$ $\mu$-a.e. for any function $f$ in $L^2(\mu )$. As a consequence of our main theorems, we also deal with the so-called one-sided weighted ergodic Hilbert transforms.

References in corpus (1)

• On random almost periodic trigonometric polynomials and applications to ergodic theory