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2020 Fiscal Year Final Research Report

The study of fractional operator in Harmonic Analysis

Research Project

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Project/Area Number 18K13434
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionFukushima National College of Technology

Principal Investigator

Takeshi Iida  福島工業高等専門学校, 一般教科, 准教授 (60633435)

Project Period (FY) 2018-04-01 – 2021-03-31
Keywords荷重理論 / Morrey空間 / Orlicz-Morrey空間 / Orlicz分数冪極大作用素 / 分数冪積分作用素
Outline of Final Research Achievements

There are three main research results:(1)We showed that the sufficient condition for the Orlicz-fractional maximal operators of the Hardy-Littlewood-Sobolev type inequality is also necessary. (2)We showed that the condition of (1) is also a sufficient condition of the Adams type inequality for the Orlicz-fractional maximal operator in Morrey space. (3)Based on (1) and (2) research results, we constructed the theory of the weighted norm inequalities of the Orlicz fractional maximal operator in the Orlicz-Morrey space, including the case of multilinear.

Free Research Field

調和解析

Academic Significance and Societal Importance of the Research Achievements

2013年にOrlicz分数冪極大作用素に対するHardy-Littlewood-Sobolev型不等式が成り立つための十分条件が示されたが、本研究(1)によってそれが必要条件でもあることが示された。(1)の研究成果は、Orlicz分数冪極大作用素の多くの関数空間の有界性を議論する上で基礎理論であり、今後の研究の更なる発展が見込まれる。例えば(2)と(3)の研究はMorrey空間上のOrlicz分数冪極大作用素の有界性に対する(1)の発展的研究である。

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Published: 2022-01-27  

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