Mathematische Annalen

, Volume 348, Issue 4, pp 797–813

Local Hardy–Littlewood maximal operator


DOI: 10.1007/s00208-010-0499-1

Cite this article as:
Lin, CC. & Stempak, K. Math. Ann. (2010) 348: 797. doi:10.1007/s00208-010-0499-1


In this article we define and investigate a local Hardy–Littlewood maximal operator in Euclidean spaces. It is proved that this operator satisfies weighted Lp, p > 1, and weighted weak type (1,1) estimates with weight function \({w \in A^p_{\rm{loc}}}\), the class of local Ap weights which is larger than the Muckenhoupt Ap 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

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