Boundedness of commutators on Hardy type spaces |
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Authors: | Lu Shanzhen Wu Qiang and Yang Dachun |
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Institution: | Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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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 |
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Keywords: | singular integral commutator Lipschitz space Hardy space Lebesgue space weak space Herz space atom Riesz potential |
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