On Hardy-Littlewood Inequality for Brownian Motion on Riemannian Manifolds (original) (raw)

This work investigates the Hardy-Littlewood inequality in the context of Brownian motion on Riemannian manifolds characterized by polynomial volume growth. The authors establish a sharp analogue of the classical theorem, indicating a fundamental relationship between the volume growth conditions and the escape rates of Brownian motion. Key results include the demonstration that under specific curvature conditions of the manifold, the upper radius exhibit characteristics similar to those predicted by classical results, thus broadening the applicability of the original inequality in probabilistic contexts.