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Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators

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Title: Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators
Authors: Terasawa, Yutaka Browse this author
Keywords: Hardy-Littlewood maximal operator
weak type (1
1) estimate
operator norm
outer measure
Issue Date: 2004
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 692
Start Page: 1
End Page: 13
Abstract: We will introduce the $k$ times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for $k>0$. We will prove the $k$ times modified centered Hardy-Littlewood maximal operator is weak type $(1,1)$ bounded with constant $1$ when $k \ge 2$ if the Radon measure of the space has ``continuitiy'' 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69497
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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