从Lp(Rn+,ω(x))到Lp(Rm+)的Hardy型奇异积分算子的(p,p)型范数

J4 ›› 2009, Vol. 47 ›› Issue (6): 1130-1134.

从L^p(Rⁿ₊,ω(x))到L^p(R^m_+⁾的Hardy型奇异积分算子的(p,p)型范数

洪勇

广东商学院数学与计算科学学院, 广州 510320

收稿日期:2009-02-16 出版日期:2009-11-26 发布日期:2010-01-07
通讯作者: 洪勇 E-mail:hongyong@gdcc.edu.cn.

On the (p,p) Type Norm of Hardy’s Type Singular IntegralOperator from L^p(Rⁿ₊,ω(x)) to L^p(R^m_+⁾

HONG Yong

College of |Mathematics and Computer Science, Guangdong University of Business Studies, Guangzhou 510320, China

Received:2009-02-16 Online:2009-11-26 Published:2010-01-07
Contact: HONG Yong E-mail:hongyong@gdcc.edu.cn.

摘要/Abstract

摘要：

设||x||_λ=(x^λ₁+x^λ₂+…+x^λ_n)^1/λ(x∈Rⁿ₊), ω(x)是非负可测函数, 定义带参数r的从L^p(Rⁿ₊,ω(x))到L^p(R^m₊₎的Hardy的Hardy型奇异积分算子T_r利用权函数方法, 讨论了T_r的(p,p)型范数, 并得到其范数的参数表达式.

关键词: Hardy型奇异积分算子, (p,p)型范数, Γ函数

Abstract:

Suppose ||x||_λ=(x^λ₁+x^λ₂+…+x^λ_n)^1/λ(x∈Rⁿ₊), ω(x)≥0 is a measurable function, Hardy’s type singular integral operator T_r with parameter r from L^p(Rⁿ₊,ω(x)) to L^p(R^m_+⁾ is defined as the (p,p) type norm of operator T_r is obtained by estimating the weight function.

Key words: Hardy’s type singular integral operator, (p,p) type norm, Γ function

中图分类号:

O178

洪勇. 从L^p(Rⁿ₊,ω(x))到L^p(R^m_+⁾的Hardy型奇异积分算子的(p,p)型范数[J]. J4, 2009, 47(6): 1130-1134.

HONG Yong. On the (p,p) Type Norm of Hardy’s Type Singular IntegralOperator from L^p(Rⁿ₊,ω(x)) to L^p(R^m_+⁾[J]. J4, 2009, 47(6): 1130-1134.

从L^p(Rⁿ₊,ω(x))到L^p(R^m_+⁾的Hardy型奇异积分算子的(p,p)型范数

On the (p,p) Type Norm of Hardy’s Type Singular IntegralOperator from L^p(Rⁿ₊,ω(x)) to L^p(R^m_+⁾

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