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2015 Fiscal Year Final Research Report

Research on Fourier integrals and singular integrals

Research Project

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Project/Area Number 25400130
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKanazawa University

Principal Investigator

Sato Shuichi  金沢大学, 学校教育系, 教授 (20162430)

Project Period (FY) 2013-04-01 – 2016-03-31
KeywordsFourier 級数 / 特異積分
Outline of Final Research Achievements

We considered Littlewood-Paley operators and singular integral operators in general homogeneous groups including the Heisenberg group and proved that those operators have mapping properties similar to the ones that are known on the Euclidean spaces. Here, the kernels of the operators are assumed to have minimal size conditions and cancellation properties. Also, we have succeeded to characterize the Sobolev spaces on the Euclidean spaces by some Littlewood-Paley operators (IllinoisJ. Math. 58(4)).

Free Research Field

解析学基礎

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Published: 2017-05-10  

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