各向异性函数空间上的多线性算子的估计及其应用

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.

Estimates for multilinear operators on anisotropic function spaces and their applications

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.