HEAT KERNEL BASED DECOMPOSITION OF SPACES OF DISTRIBUTIONS IN THE FRAMEWORK OF DIRICHLET SPACES

被引:0
作者
Kerkyacharian, Gerard [1 ]
Petrushev, Pencho [2 ]
机构
[1] Univ Paris Diderot, CNRS, UMR 7599, Lab Probabilites & Modeles Aleatoires, F-75013 Paris, France
[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
基金
美国国家科学基金会;
关键词
Heat kernel; functional calculus; frames; Besov spaces; Triebel-Lizorkin spaces; LOCALIZED POLYNOMIAL FRAMES; WEIGHTED TRIEBEL-LIZORKIN; BESOV-SPACES; HARDY-SPACES; OPERATORS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincare inequality. This leads to a heat kernel with small time Gaussian bounds and Holder continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows the development of Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifolds, and other settings.
引用
收藏
页码:121 / 189
页数:69
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