Powers of Distances to Lower Dimensional Sets as Muckenhoupt Weights

By H. Aimar, M. Carena, Ricardo G. Dur'an, M. Toschi. 2013

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Let (X, d, μ) be an Ahlfors metric measure space. We give sufficient conditions on a closed set $${F \subseteqq X}$$F⫅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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/32b5e1ef594bff7a4f62f856c62439d38c605942