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Acta Mathematica Hungarica

, Volume 143, Issue 1, pp 119–137 | Cite as

Powers of Distances to Lower Dimensional Sets as Muckenhoupt Weights

  • H. Aimar
  • M. CarenaEmail author
  • R. Durán
  • M. Toschi
Article

Abstract

Let (X, dμ) 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.

Keywords and phrases

Ahlfors space Hardy–Littlewood maximal operator Muckenhoupt weight Hausdorff measure 

Mathematics Subject Classification

primary 28A25 secondary 28A78 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FIQ-UNL)Santa FeArgentina
  2. 2.Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FHUC-UNL)Santa FeArgentina
  3. 3.Instituto de Investigaciones Matemáticas “Luis A. Santaló” (CONICET-UBA), Departamento de Matemática (UBA)Buenos AiresArgentina

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