2024-03-29T12:23:13Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694972022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operatorsTerasawa, YutakaHardy-Littlewood maximal operatorweak type (11) estimateoperator normouter measure410We 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69497info:doi/10.14943/83843https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69497/1/pre692.pdfHokkaido University Preprint Series in Mathematics6921132004engpublisher