Weighted inequalities and a.e. convergence for Poisson integrals in light-cones

Damek, E.
Garrigos Aniorte, Gustavo
Harboure, Eleonor Ofelia
Torrea Hernández, José Luis

Open link

Publication date

November 2006

DOI

10.1007/s00208-006-0023-9

Publisher

Springer Science and Business Media LLC

Journal

Mathematische Annalen

Abstract

We show that the Poisson maximal operator for the tube over the light-cone, P*, is bounded in the weighted space L p (w) if and only if the weight w(x) belongs to the Muckenhoupt class A p . We also characterize with a geometric condition related to the intrinsic geometry of the cone the weights v(x) for which P* is bounded from L p (v) into L p (u), for some other weight u(x) > 0. Some applications to a.e. restricted convergence of Poisson integrals are given.Fil: Damek, E.. University of Wrocław; PoloniaFil: Garrigos Aniorte, Gustavo. Universidad Autónoma de Madrid; EspañaFil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Apli...