中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (2): 20-24.

• 研究论文 • 上一篇    下一篇

非齐性空间上新型奇异积分算子的弱(1,1)不等式

谭超强   

  1. (汕头大学理学院数学系,广东 汕头 515063)
  • 收稿日期:2010-03-07 修回日期:1900-01-01 出版日期:2011-03-25 发布日期:2011-03-25

Weak (1,1) Inequality for New Type Singular Integral Operators on Nonhomogeneous Spaces

TAN Chaoqiang   

  1. (Department of Mathematics, Shantou University, Shantou 515063, China)
  • Received:2010-03-07 Revised:1900-01-01 Online:2011-03-25 Published:2011-03-25

摘要: 经典的奇异积分算子是满足大小条件和光滑性条件的L2有界线性算子,而该类算子的其中一个重要结论是满足弱(1,1)不等式。在非双倍测度空间上定义一类新型的奇异积分算子,并且证明该类算子也满足弱(1,1)不等式,推广Duong类奇异积分算子理论到非双倍测度的情形。

关键词: 增长性条件, 奇异积分算子, 弱(1, 1)不等式

Abstract: It is well-known that the classical singular integral operators are linear L2 bounded operators that satisfy the size and smoothness conditions. An important property of these operators is that they satisfy the weak (1,1) inequality. A new type class of singular integral operators on nonhomogeneous spaces is defined, and the weak (1,1)inequality is proved, which extend Duong's results to the nonhomogeneous spaces.

Key words: growth condition, singular integral operators, weak(1, 1)inequality

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