, Volume 348, Issue 4, pp 797-813
Date: 03 Mar 2010

Local Hardy–Littlewood maximal operator

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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.

Research of C.-C. Lin supported by NSC and NCTS of Taiwan
To the memory of Józef Marcinkiewicz on the centenary of his birth.