Reverse Holder inequalities. Some recent results and extensions to LCA groups

EZEQUIEL RELA

Bilbao

Seminario; Análisis & PDE seminar; 2018

BCAM

We present sharp quantitative weighted norm inequalitiesfor the Hardy-Littlewood maximal function in the context of LocallyCompact Abelian Groups, obtaining an improved version of the so-calledBuckley´s Theorem. On the way, we prove a precise reverse Holderinequality for Muckenhoupt A1 weights and provide a valid version ofthe open property" for Muckenhoupt Ap weights.