Morrey spaces and weighted norm inequalities
| Project/Area Number |
23540187
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TANAKA Hitoshi 東京大学, 数理(科)学研究科(研究院), 助教 (70422392)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Morrey space / wieghted norm inequality / Riesz potential / positibe operator / Morrey空間 / 加重付ノルム不等式 / 正作用素 / 最大作用素 / 分数積分作用素 / martinngale / 方向極大作用素 / 多重Morreyノルム / 多重線形分数積分作用素 / Olsenの加重付きノルム不等式 / 二つの加重付きノルム不等式 / 斉次測度空間 |
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| Research Abstract |
In this research, a theory of weights for multilinear fractional integral operators and multi(sub)linear fractional maximal operators in the framework of Morrey spaces is developed. Natural sufficient conditions for the one and two weight inequalities of these operators are given, and, as a corollary, the Olsen inequality for multilinear fractional integral operators is obtained.
The local trace inequality for potential type integral operators in the framework of Morrey spaces is studied and the sufficient conditions for the norm inequality with a locally finite nonnegative Borel measure of potential type integral operators to hold are given. Necessary condition and sufficient condition for two-weight norm inequalities on Morrey spaces to hold are given for the Hardy-Littlewood maximal operator.Necessary and sufficient condition is also verified for the power weights.
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Report
(4 results)
Research Products
(34 results)
