Local Maximal Function and Weights in a General Setting

HARBOURE, E; SALINAS, O; VIVIANI, B

MATHEMATISCHE ANNALEN

SPRINGER

Lugar: Berlin; Año: 2014 vol. 358 p. 609 - 628

0025-5831

For a proper open set Ω immersed in a metric space with the weak homogeneity property, and given a measure μ doubling on a certain family of balls lying ?well inside? of Ω , we introduce a local maximal function and characterize the weights w for which it is bounded on Lp(Ω,wdμ) when 1<p<∞ and of weak type (1,1) . We generalize previous known results and we also present an application to interior Sobolev?s type estimates for appropriate solutions of the differential equation Δmu=f, satisfied in an open proper subset Ω of Rn. Here, the data fbelongs to some weighted Lpspace that could allow functions to increase polynomially when approaching the boundary of Ω .