Acta Mathematica Sinica

, Volume 22, Issue 1, pp 105–114

Boundedness of Some Marcinkiewicz Integral Operators Related to Higher Order Commutators on Hardy Spaces


DOI: 10.1007/s10114-005-0545-1

Cite this article as:
Lu, S.Z. & Xu, L.F. Acta Math Sinica (2006) 22: 105. doi:10.1007/s10114-005-0545-1


In this paper, the authors study the boundedness properties of \( \mu ^{m}_{{\Omega ,b}} \) generated by the function b ∈ Lipβ(ℝn)(0 < β ≤ 1/m) and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces \( H^{p}_{{b^{m} ,s}} {\left( {\mathbb{R}^{n} } \right)} \) and the Herz–Hardy type spaces \( H_{{b^{m} }} \dot{K}^{{\alpha ,p}}_{q} {\left( {\mathbb{R}^{n} } \right)} \).


Marcinkiewicz integral Higher order commutator Lipshcitz space Hardy type space Herz space 

MR (2000) Subject Classification

42B20 42B25 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Normal UniversityBeijing 100875P. R. China

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