Morrey spaces and weighted norm inequalities

莫雷空间和加权范数不等式

• 批准号: 23540187
• 负责人: TANAKA Hitoshi
• 金额: $ 2.33万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540187/
• 关键词: 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

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.

本文在Morrey空间的框架下，建立了多线性分数次积分算子和多（次）线性分数次极大算子的权理论。给出了这些算子的一个和两个权不等式的自然充分条件，作为推论，得到了多线性分数次积分算子的Olsen不等式，在Morrey空间框架下研究了势型积分算子的局部迹不等式，得到了势型积分算子的具有局部有限非负Borel测度的范数不等式成立的充分条件给出对Hardy-Littlewood极大算子给出了Morrey空间上双权范数不等式成立的充分必要条件，并证明了幂权不等式成立的充分必要条件.

项目成果

Weighted norm inequalities for multilinear fractional operators on Morrey spaces

• DOI: 10.4064/sm205-2-2
• 发表时间: 2011
• 期刊: Studia Mathematica
• 影响因子: 0.8
• 作者: Takeshi Iida;Enji Sato;Y. Sawano;Hitoshi Tanaka

A new Beale-Kato-M ajda criteria for the 3D magneto-micropolar fluid equations in Orlicz-Morrey spaces

Orlicz-Morrey 空间中 3D 磁微极流体方程的新 Beale-Kato-M ajda 准则

• 发表时间: 2012
• 期刊: Math. Methods Appl. Sci
• 作者: Gala S.;Sawano Y. and Tanaka H
• 通讯作者: Sawano Y. and Tanaka H

Orlicz–Morrey Spaces and Fractional Operators

• DOI: 10.1007/s11118-011-9239-8
• 发表时间: 2012-05
• 期刊: Potential Analysis
• 影响因子: 1.1
• 作者: Y. Sawano;Satoko Sugano;Hitoshi Tanaka

A Characterization of Two-Weight Trace Inequalities for Positive Dyadic Operators in the Upper Triangle Case

• DOI: 10.1007/s11118-013-9379-0
• 发表时间: 2013-02
• 期刊: Potential Analysis
• 影响因子: 1.1
• 作者: Hitoshi Tanaka

Directional maximal operators and radial weights on the plane

平面上的方向最大算子和径向权重

• 发表时间: 2014
• 期刊: Bull. Austral. Math. Soc
• 作者: M. Hojo;W. Takahashi;松本裕行;Saito H . and Tanaka H
• 通讯作者: Saito H . and Tanaka H