Weighted ergodic averages along subpolynomials in Hardy fields and applications

We establish new pointwise convergence results for weighted ergodic averages along sequences of the form \( (\lfloor a(n) \rfloor)_{n \in \mathbb{N}}, \) where $a(x)$ is a subpolynomial function in a Hardy field. For example, we establish pointwise convergence of logarithmic averages along sequenc