, Volume 45, Issue 8, pp 984-997

Boundedness of commutators on Hardy type spaces

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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