title: Differentiation of integrals in higher dimensions.
abstract: We prove a localization principle for directional maximal operators in L(p)(R(n)), with p > 1. The resulting bounds, which we conjecture hold for the largest possible class of directions, imply Lebesgue-type differentiation of integrals over tubes that point in the given directions.
authors.affiliation: Instituto de Ciencias Matemáticas (Consejo Superior de Investigaciones Científicas-Universidad Autónoma de Madrid-Universidad Carlos III de Madrid-Universidad Complutense de Madrid), 28049 Madrid, Spain.
authors.forename: Javier
authors.initials: J
authors.lastname: Parcet
authors.forename: Keith M
authors.initials: KM
authors.lastname: Rogers