Local fractional and singular integrals on open subsets

Abstract

For a proper open set $Omega$ immersed in a metric space with the weak homogeneity property, and given a measure $mu$ doubling on a certain family of balls lying ``well inside´´ of $Omega$, we introduce local operators of singular and fractional type and study their boundedness properties on weighted $L^p(Omega)$, $1leq p < infty$, for weights in local Muckenhoupt classes.