2013 Fiscal Year Final Research Report
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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| Keywords | Morrey space / wieghted norm inequality / Riesz potential / positibe operator |
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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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Research Products
(19 results)
