Mathematische Annalen

, Volume 348, Issue 4, pp 797–813 | Cite as

Local Hardy–Littlewood maximal operator



In this article we define and investigate a local Hardy–Littlewood maximal operator in Euclidean spaces. It is proved that this operator satisfies weighted L p , p > 1, and weighted weak type (1,1) estimates with weight function \({w \in A^p_{\rm{loc}}}\), the class of local A p weights which is larger than the Muckenhoupt A p class. Also, the condition \({w \in A^p_{\rm{loc}}}\) turns out to be necessary for the weighted weak type (p,p), p ≥ 1, inequality to hold.

Mathematics Subject Classification (2000)

Primary 42B25 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsNational Central UniversityChung-LiTaiwan, Republic of China
  2. 2.Instytut Matematyki i InformatykiPolitechnika WrocławskaWrocławPoland
  3. 3.Katedra Matematyki i Zastosowań InformatykiPolitechnika OpolskaOpolePoland

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