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Boundedness of commutators on Hardy type spaces
Authors:Lu Shanzhen  Wu Qiang and Yang Dachun
Institution:Department of Mathematics, Beijing Normal University, Beijing 100875, China
Abstract:Let b,T] be the commutator of the functionb ∈ Lip β (ℝ 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 cases
Keywords:singular integral  commutator  Lipschitz space  Hardy space  Lebesgue space  weak space  Herz space  atom  Riesz potential
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