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Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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