2017年
Hardy spaces for ball quasi-Banach function spaces
Dissertationes Mathematicae
- ,
- ,
- ,
- 巻
- 525
- 号
- 525
- 開始ページ
- 1
- 終了ページ
- 102
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.4064/dm750-9-2016
- 出版者・発行元
- POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
This article unifies the theory for Hardy spaces built on Banach lattices on ℝn satisfying certain weak conditions on indicator functions of balls. The authors introduce a new family of function spaces, named the ball quasi-Banach function spaces, to define Hardy type spaces. The ones in this article extend classical Hardy spaces and include various known function spaces, for example, Hardy–Lorentz spaces, Hardy–Herz spaces, Hardy–Orlicz spaces, Hardy–Morrey spaces, Musielak–Orlicz–Hardy spaces, variable Hardy spaces and variable Hardy–Morrey spaces. Among them, Hardy–Herz spaces are shown to naturally arise in the context of any function spaces above. The example of Hardy–Morrey spaces shows that the absolute continuity of the quasi-norm is not necessary, which is used to guarantee the density of the set of functions having compact supports in Hardy spaces for ball quasi-Banach function spaces, but the decomposition result on these Hardy-type spaces never requires this absolute continuity of the quasi-norm. Moreover, via assuming that the powered Hardy–Littlewood maximal operator satisfies certain Fefferman–Stein vector-valued maximal inequality as well as it is bounded on the associate space, the atomic characterizations of Hardy type spaces are obtained. Although the results are based on the rather abstract theory of function spaces, they improve and extend the results for Orlicz spaces and Musielak–Orlicz spaces. Moreover, local Hardy type spaces and Hardy type spaces associated with operators in this setting are also studied.
- リンク情報
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- DOI
- https://doi.org/10.4064/dm750-9-2016
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000408332900001&DestApp=WOS_CPL
- 共同研究・競争的資金等の研究課題
- フーリエ解析学の新展開-関数空間の分割理論の深化と応用
- Scopus
- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85027844426&origin=inward
- Scopus Citedby
- https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85027844426&origin=inward
- ID情報
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- DOI : 10.4064/dm750-9-2016
- ISSN : 0012-3862
- eISSN : 1730-6310
- SCOPUS ID : 85027844426
- Web of Science ID : WOS:000408332900001