Differentiation of integrals in higher dimensions

作者：Parcet Javier; Rogers Keith M^*

来源：Proceedings of the National Academy of Sciences, 2013, 110(13): 4941-4944.

DOI：10.1073/pnas.1218928110

• fundamental theorem of calculus
• lacunary directions
• maximal operators

We prove a localization principle for directional maximal operators in L-p(R-n), with p %26gt; 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.

• 出版日期2013-3-26