吉首大学学报(自然科学版)

• 数学 •    下一篇

具有齐次核的奇异积分算子的范数及其应用

洪勇   

  1. (广东财经大学统计与数学学院,广东 广州 510320)
  • 出版日期:2017-09-25 发布日期:2017-11-02

Norm of a Singular Integral Operator with Homogeneous Kernel and Its Application

HONG Yong   

  1. (College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China)
  • Online:2017-09-25 Published:2017-11-02
  • About author:HONG Yong (1959—),male,was born in Zhaotong City,Yunnan Province,profess of College of Statistics and Mathematics,Guangdong University of Finance and Economics;research areas are harmonic analysis and analytic inequality.
  • Supported by:

    National Natural Science Foundation of China (61300204)

摘要:

K(x,y)满足K(x,y)=K(y,x)和K(tx,ty)=tλK(x,y).定义奇异积分算子TT(f)(y)=∫+∞0K(x,y)f(x)dx,y∈(0,+∞),推导出获得算子T的范数的充分条件.利用这个结果,证明了一些新的积分不等式.

关键词: 对称齐次核, 奇异积分算子, 范数, 有界算子

Abstract:

Suppose K(x,y) satisfies K(x,y)=K(y,x) and K(tx,ty)=tλK(x,y).Define the singular integral operator T as T(f)(y)=∫+∞0K(x,y)f(x)dx,y∈(0,+∞).Sufficient conditions guaranteeing the norm of T are obtained.Some new integral inequalities are proved from these results.

Key words: symmetric homogeneous kernel, singular integral operator, norm, bounded operator

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