Boundedness of commutators on Hardy type spaces  

作　　者：陆善镇 吴强 杨大春 

出　　处：《Science China Mathematics》2002年第8期984-997,共14页中国科学：数学（英文版）

基　　金：This work was supported by the National 973 Project of China (Grant No.G19990751); the National Natural Science Foundation of China (Grant No. 19131080) ; the State Education Department Foundation of China (Grant No. 20010027002).

摘　　要：Let [b,T] be the commutator of the functionb ∈ Lip β (? n ) (0 <β ? 1)and the Calderón-Zygmund singular integral operatorT. The authors study the boundedness properties of [b,T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme casesLet [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 ＜β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases.

关 键 词：singular integral  commutator  Lipschitz space  HARDY space  LEBESGUE space  weak space  HERZ space  atom  RIESZ potential. 

分 类 号：O177[理学—数学]