We study the a.e. convergence of the Cesàro-$(1+\alpha)$ ergodic averages and the a.e. existence in the Cesàro-$\alpha$ sense of the ergodic Hilbert transform associated with Cesàro bounded flow and $-1\lt \alpha \leq 0$.

We consider positive invertible Lamperti operators Tf(x)=h(x)Φf(x) such that Φ has no periodic part. Let An,T be the sequence of averages of T and MT the ergodic maximal operator. It is obvious that if MT is bounded on some Lp, 1

Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏ ...

Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all ...

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for ...