Seminario Análisis y Aplicaciones
Sharp L^p bounds for the Hardy-Littlewood maximal operator in hyperbolic settings
Ponente: Nikolaos Chalmoukis (Università degli studi di Milano Bicocca)Fecha: viernes 07 de noviembre de 2025 - 11:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
Let (X, d) be a Gromov hyperbolic space equipped with a locally finite Borel measure that is locally doubling and of exponential growth. In this setting, we establish sharp weak type bounds for the centered Hardy–Littlewood maximal operator. Our results aim to clarify how the mapping properties of the Hardy–Littlewood maximal operator depend on the geometry of a space which is globally negatively curved. In particular, the bounds apply to Cartan-Hadamard manifolds of pinched negative curvature and symmetric spaces of noncompact type and rank one. A key ingredient in the proof is a discretization procedure, which allows us to approximate in a convenient way an arbitrary Gromov hyperbolic space by a class of graphs which we call spider’s webs.
This is a joint work with S. Meda and F. Santagati.
