, Volume 22, Issue 1, pp 105-114
Date: 16 Jun 2005

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

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Abstract

In this paper, the authors study the boundedness properties of \( \mu ^{m}_{{\Omega ,b}} \) generated by the function b ∈ Lip β (ℝn)(0 < β ≤ 1/m) and the Marcinkiewicz integrals operator μ Ω . 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 \( H_{{b^{m} }} \dot{K}^{{\alpha ,p}}_{q} {\left( {\mathbb{R}^{n} } \right)} \) .

Supported by the National 973 Project (G. 19990751) and the SEDF (20010027002)