首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Classes of Hardy spaces associated with operators, duality theorem and applications
Authors:Lixin Yan
Institution:Department of Mathematics, Zhongshan University, Guangzhou, 510275, People's Republic of China
Abstract:Let $ L$ be the infinitesimal generator of an analytic semigroup on $ L^2({\mathbb{R}}^n)$ with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space $ H^1_L({\mathbb{R}}^n)$ and a $ {\rm BMO}_L({\mathbb{R}}^n)$ space associated with the operator $ L$ were introduced and studied. In this paper we define a class of $ H^p_L({\mathbb{R}}^n)$ spaces associated with the operator $ L$ for a range of $ p<1$ acting on certain spaces of Morrey-Campanato functions defined in New Morrey-Campanato spaces associated with operators and applications by Duong and Yan (2005), and they generalize the classical $ H^p({\mathbb{R}}^n)$ spaces. We then establish a duality theorem between the $ H^p_L({\mathbb{R}}^n)$ spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on $ H^p_L({\mathbb{R}}^n)$ and give the inclusion between the classical $ H^p({\mathbb{R}}^n)$ spaces and the $ H^p_L({\mathbb{R}}^n)$ spaces associated with operators.

Keywords:
点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号