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

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On the (p,p) Type Norm of Hardy’s Type Singular IntegralOperator from Lp(Rn+,ω(x)) to Lp(Rm+)

HONG Yong   

  1. 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.

Abstract:

Suppose ||x||λ=(xλ1+xλ2+…+xλn)1/λ(x∈Rn+), ω(x)≥0 is a measurable function, Hardy’s type singular integral operator Tr with parameter r from Lp(Rn+,ω(x)) to Lp(Rm+) is defined as the (p,p) type norm of operator Tr is obtained by estimating the weight function.

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

CLC Number: 

  • O178