Abstract
AbstractIn this paper we prove a general ergodic theorem for ergodic and measure-preserving actions of \(\mathbb{R}^d\) on standard Borel spaces. In particular, we cover R.L. Jones’ ergodic theorem on spheres. Our main theorem is concerned with almost everywhere convergence of ergodic averages with respect to homogeneous dilations of certain Rajchman measures on \(\mathbb{R}^d\). Applications include averages over smooth submanifolds and polynomial curves.1KeywordsPointwise ergodic theoremsFourier dimension of a measuremaximal inequalities
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