Asymptotically sharp Reverse H\"older inequalities for flat weights

EZEQUIEL RELA

Madrid

Seminario; Seminario del Departamento de Matemática de la Universidad Autónoma de Madrid; 2018

UAM

We present reverse Holder inequalities for Muckenhoupt weights in Rn withan asymptotically sharp behavior for at weights, namely A1 weights withFujii-Wilson constant (w)A1 ! 1+. That is, the local integrability exponentin the reverse Holder inequality blows up as the weight becomes nearly constant.This is expressed in a precise and explicit computation of the constantsinvolved in the reverse Holder inequality. The proofs avoid BMO methodsand rely instead on precise covering arguments. We also prove sharp endpointweak-type reverse Holder inequalities and consider further extensionsto general non-doubling measures and multiparameter weights. This is a jointwork with Ioannis Parissis from Universidad del Pas Vasco UPV/EHU andIkerbaske.