Boundedness of Some Marcinkiewicz Integral Operators Related to Higher Order Commutators on Hardy Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Shan Zhen Lu Li Fang Xu

Affiliation:	(1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China

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)

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