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arXiv · 1306.0893

Powers of distances to lower dimensional sets as Muckenhoupt weights

Hugo Aimar·Marilina Carena·Ricardo Durán·Marisa Toschi
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Abstract

Let $(X,d,μ)$ be an Ahlfors metric measure space. We give sufficient conditions on a closed set $F\subseteq X$ and on a real number $β$ in such a way that $d(x,F)^β$ becomes a Muckenhoupt weight. We give also some illustrations to regularity of solutions of partial differential equations and regarding some classical fractals.

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Hugo Aimar, Marilina Carena, Ricardo Durán, Marisa Toschi. 2013-06-03. Powers of distances to lower dimensional sets as Muckenhoupt weights. https://arxiv.org/abs/1306.0893

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