数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 764-772.

• 论文 • 上一篇    下一篇

齐型空间上带非光滑核的奇异积分算子的双权不等式

  

  1. (信息工程大学应用数学系 |郑州 450002)
  • 收稿日期:2007-12-16 修回日期:2008-12-13 出版日期:2009-06-25 发布日期:2009-06-25

A Two-weight Norm Inequality for Singular Integral Operators with Non-smooth Kernel on Spaces of Homogeneous Type

  1. (Department of Applied Mathematics, University of Information Engineering, Zhengzhou 450002)
  • Received:2007-12-16 Revised:2008-12-13 Online:2009-06-25 Published:2009-06-25

摘要:

该文在齐型空间( X, dμ)上建立带非光滑核的奇异积分算子的双权、弱型不等式, 即对于1< p ≤ q < ∞, 此算子是Lp( X, v)到 Lq, ∞( X, u)有界的, 只要权函数对(u, v)满足在权 u 上增加一个"Orlicz-bump" '的 Ap 型条件.

关键词: 齐型空间, 加权不等式, 奇异积分算子, 非光滑核

Abstract:

In this paper, a two-weight weak type norm inequality for singular integral operators with non-smooth kernel is established on spaces of homogeneous type. The authors prove that the operators in question are bounded from Lp(X, v) to Lq( X, u) with 1< p ≤  q <∞, provided that the pair of weights (u, v) verifies an Ap-type condition with an '`Orlicz-bump'' on the weight u.

Key words: Spaces of homogeneous type, Norm inequality, Singular integral operator, Non-smooth kernel

中图分类号: 

  • 42B20