2013 Fiscal Year Final Research Report
Functional spaces of two variable exponents on metric measure spaces
| Project/Area Number |
23740108
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Oita University |
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Principal Investigator |
OHNO Takao 大分大学, 教育福祉科学部, 准教授 (40508511)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 変動指数をもつ関数空間 / 距離空間 / Sobolevの不等式 / Hajlasz空間 / ポテンシャル論 |
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| Research Abstract |
Our aim is to study Musielak-Orlicz Sobolev spaces on metric measure spaces. We consider a Hajlasz type condition and a Newtonian type condition. We prove that Lipschitz continuous functions are dense as well as other basic properties. We study the relationship between these spaces, and discuss Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood maximal operator, we establish a generalization of Sobolev's inequality for Sobolev functions in Musielak-Orlicz-Hajlasz spaces.
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