Differentiation of integrals in higher dimensions.
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- Record sourced from PubMed, PMID 23479658.
- Also identified by DOI 10.1073/pnas.1218928110 and PMC identifier 3612610.
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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.