摘要
设A是Rn上的各向异性伸缩, L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lwp(Rn)到无权的各向异性Hardy空间HAp (Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOAw(Rn)得到包含关系:BMOAw(Rn)■(H1A(Rn))*.作为应用,对加权各向异性BMO函数b和各向异性Calderón-Zygmund算子T生成的交换子[T, b],得到‖[T, b](f)‖Lwp(Rn)C‖b‖BMOwA(Rn)‖f‖Lpw(Rn).以上所有结果在经典的各向齐性情形下也是新的.
Let A be an anisotropic dilation on Rn and L a general multilinear operator formed by anisotropic C alderon-Zygmund operators.We obtain the boundedness of L from weighted Lebesgue spaces to the unweighted anisotropic Hardy space.Moreover,for the anisotropic BMO space BMOA(Rn) and the weighted anisotropic BMO space BMOAw(Rn),we obtain an inclusion relationship:BMOAw(Rn)■BMOA(Rn).As an application,for the commutator [T,b] of the anisotropic Calderon-Zygmund operator T and b in BMOAw(Rn),we obtain‖T,b](f)‖Lwp(Rn)≤C‖b‖BMOAw(Rn)‖f‖Lwp(Rn).All these results are still new even in the classical isotropic setting.
作者
邱小丽
齐春燕
刘雄
李宝德
Xiaoli Qiu;Chunyan Qi;Xiong Liu;Baode Li
出处
《中国科学：数学》
CSCD
北大核心
2021年第3期499-512,共14页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11861062,11661075和11561065)资助项目。
