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Powers of Distances to Lower Dimensional Sets as Muckenhoupt Weights |
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| Authors: | H. Aimar M. Carena R. Durán M. Toschi |
| Affiliation: | 1. Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FIQ-UNL), Santa Fe, Argentina 2. Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FHUC-UNL), Santa Fe, Argentina 3. Instituto de Investigaciones Matemáticas “Luis A. Santaló” (CONICET-UBA), Departamento de Matemática (UBA), Buenos Aires, Argentina |
| Abstract: | Let (X, d, μ) be an Ahlfors metric measure space. We give sufficient conditions on a closed set ({F subseteqq 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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