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Erschienen in:
Open Access 01.12.2006 | Research Article
Outer measures and weak type
estimates of Hardy-Littlewood maximal operators
Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006
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Abstract
We will introduce the
times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for
. We will prove that the
times modified centered Hardy-Littlewood maximal operator is weak type
bounded with constant
when
if the Radon measure of the space has "continuity" in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.
times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for
. We will prove that the
times modified centered Hardy-Littlewood maximal operator is weak type
bounded with constant
when
if the Radon measure of the space has "continuity" in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.