On the convergence of nonuniform ergodic means (Q369592)

Given any semiflow \(\{T_t\}\) with an invariant measure \(\mu\), and absolutely continuous probability measures \(v\), define for any bounded function \(f\) the nonuniform averaging \[ F_tf(x)= \int^{+\infty}_0 f(T_{ts} x)\,v(ds). \] The aim of the present paper is to study the convergence of nonuniform ergodic means \(F_t f(x)\) in the space \(L^p(\mu)\) extending the previous historical approaches for bounded and unbounded functions \(f\) as well as for stochastic equations and operator semigroups. In addition the author manages to give some applications of the results obtained in the paper such as an analogue of the ergodic Wiener-Wintner theorem.