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arXiv · 1705.05072

Maximal function estimates and self-improvement results for Poincar\'e inequalities

Juha Kinnunen·Juha Lehrbäck·Antti V. Vähäkangas·Xiao Zhong
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Abstract

Our main result is an estimate for a sharp maximal function, which implies a Keith-Zhong type self-improvement property of Poincar\'e inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.

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Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas, Xiao Zhong. 2017-05-15. Maximal function estimates and self-improvement results for Poincar\'e inequalities. https://arxiv.org/abs/1705.05072

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