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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