Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type |
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| Authors: | Hugo Aimar Marilina Carena Marisa Toschi |
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| 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 |
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| Abstract: | We give sufficient conditions on a real number β and on a closed set F in a general space of homogeneous type (X,d,μ) in such a way that μ(B(x,d(x,F)))β becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes 1-Ahlfors regular. |
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| Keywords: | Muckenhoupt weights Spaces of homogeneous type Ahlfors spaces Hardy&ndash Littlewood maximal operator |
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