具有非倍测度的参数型Marcinkiewicz交换子在Morrey空间的有界性  

Boundedness of Commutators of Parameter Marcinkiewicz Integrals on Morrey Spaces With Non-doubling Measures

作　　者：逯光辉 周疆[1] 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐新疆830046

出　　处：《数学进展》2015年第1期73-83,共11页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11261055;No.11161044);新疆维吾尔自治区自然科学基金资助项目(N2011211A005;No.BS120104)

摘　　要：本文证明了由参数型Marcinkiewicz积分M^p和Lipschitz函数b生成的交换子M_b^p的有界性。在M的核函数满足较强的H(o|¨)rmander条件下,证明了M_b^p不仅从Morrey空间M_p^q(μ)到Morrey空间M_t^s(μ)有界,从Morrey空间M_p^q(μ)到Lipschitz空间Lip_(β-n/p)(μ)有界,而且从Morrey空间M_p^q(μ)到RBMO(μ)有界.In this paper,the authors prove the boundedness of the commutator M_b^p generated by the parameter Marcinkiewicz integral M^p with Lipschitz function b.Under the assumption that the kernel of M.satisfies certain slightly stronger H(o|¨)rmander-type condition,the authors prove that M_b^p is bounded from the Morrey space M_q^p(μ) to the Morrey space M_t^s(μ),from the Morrey space M_q^p(μ) to the Lipschitz space Lip_(β-n/p)(μ),and from the Morrey space A_q^p(μ) to the space RBMO(μ).

关 键 词：非倍测度 参数型MARCINKIEWICZ积分 MORREY空间 

分 类 号：O177[理学—数学]