Differentiation of integrals in higher dimensions.

Parcet, Javier; Rogers, Keith M · Proc Natl Acad Sci U S A · 2013

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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.