摘要
众所周知,Calderón-Zygmund奇异积分算子理论及刻画这些算子有界性的各种函数空间的实变理论因其在调和分析和偏微分方程等数学分支中有重要的应用而成为现代调和分析的主要内容之一.然而,经典函数空间的实变理论已不再适用于刻画相关于某些比Laplace算子更一般的微分算子的奇异积分算子的有界性.因此,对不同的算子发展与其相适应的、能刻画其相关奇异积分算子有界性的函数空间的实变理论已成为调和分析中近年来十分活跃的研究方向之一.本文主要研究n维欧氏空间Rn、Rn中的强Lipschitz区域或更一般的带双倍测度的度量空间上与包括二阶散度型椭圆算子和Schr?dinger算子在内的微分算子相关的(Musielak-)Orlicz-Hardy空间的实变理论及其在算子有界性中的应用.
As is well-known, because of their important applications in several branches of mathematics, such as harmonic analysis and partial differential equations, the theory of CalderSn-Zygmund singular integral operators and the real-variable theory of various function spaces, which could characterize the boundedness of those operators, turn into one of the main contents of modern harmonic analysis. However, the real-variable theory of classical function spaces has been no longer suitable for characterizing the boundedness of singular integral operators associated with some more general differential operators than Laplace operators. Thus, for different operators, it has become one of the very active research fields of harmonic analysis in recent years to develop the real-variable theory of function spaces, which are suitable to those operators and could characterize the boundedness of singular integral operators associated with those operators. In this article, we study the real- variable theory of （Musielak-）Orlicz-Hardy spaces associated with some differential operators, including second- order divergence form elliptic operators and SchrSdinger operators as special cases, on n-dimensional Euclidean space Rn, strongly domains of Rn or metric spaces with doubling measure, and its applications to the boundedness of operators.
出处
《中国科学：数学》
CSCD
北大核心
2015年第2期105-116,共12页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11401276)
兰州大学中央高校基本科研业务费专项资金(批准号:lzujbky-2014-18)资助项目
