齐型空间上加权Besov空间与Triebel-Lizorkin空间的Tb定理  

Tb theorem for weighted Besov spaces and Triebel-Lizorkin spaces on homogeneous spaces

作　　者：刘金瑞 郑涛涛 肖燕梅 LIU Jinrui;ZHENG Taotao;XIAO Yanmei(School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,Zhejiang,China)

机构地区：[1]浙江科技大学理学院,杭州310023

出　　处：《浙江科技学院学报》2024年第1期1-12,共12页Journal of Zhejiang University of Science and Technology

基　　金：国家自然科学基金项目(11626213);浙江省自然科学基金项目(LQ17A010002)。

摘　　要：【目的】齐型空间自然地包含了欧氏空间R^(n)、光滑紧Riemann流形及Lipschitz区域的边界等,拟在齐型空间上建立奇异积分算子在加权Besov空间与Triebel-Lizorkin空间上有界的Tb定理。【方法】通过离散Calderón再生公式和几乎正交估计建立加权Besov空间与加权Triebel-Lizorkin空间的Plancherel-P8lya特征刻画,以保证函数空间的范数独立于恒等逼近的选取。【结果】获得了齐型空间上Calderón-Zygmund奇异积分算子在加权Besov空间及Triebel-Lizorkin空间上有界的充分条件。【结论】将欧氏空间上的Calderón-Zygmund奇异积分理论延拓到更广的齐型空间上,为奇异积分算子在函数空间上有界提供了判定方法。[Objective]Homogeneous spaces naturally contain Euclidean spaces R^(n),smooth tight Riemann manifolds,and boundaries of Lipschitz regions,etc.It is imperative to establish on homogeneous spaces the Tb theorem that singular integral operators are bounded on weighted Besov spaces and Triebel-Lizorkin spaces.[Method]Plancherel-P lya feature characterizations of weighted Besov spaces and weighted Triebel-Lizorkin spaces were established by means of discrete Calderón regeneration formulas and almost orthogonal estimation to ensure that the number of paradigms in the function space was chosen independent of the constant approximation.[Result]Sufficient conditions are obtained for Calderón-Zygmund singular integral operators on homogeneous spaces to be bounded on weighted Besov spaces as well as on Triebel-Lizorkin spaces.[Conclusion]Extending the Calderón-Zygmund theory of singular integrals on Euclidean spaces to a wider range of homogeneous spaces provides a method for determining that singular integral operators are bounded on function spaces.

关 键 词：加权Besov空间 加权Triebel-Lizorkin空间 Plancherel-P8lya特征刻画 仿增长函数 Tb定理 

分 类 号：O174.2[理学—数学]