Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2016-06-28 DOI:10.1515/agms-2017-0006

E. Saksman, Tom'as Soto

引用次数: 17

Abstract

Abstract We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

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度量空间上的Besov、triiebel - lizorkin和Sobolev空间的迹

摘要建立了定义在一般Ahlfors正则度量空间Z上的函数空间的迹定理，结果涵盖了平滑指标s < 1的triiebel - lizorkin空间和Besov空间，以及一阶Hajłasz-Sobolev空间M1,p(Z)。它们推广了欧氏集合的经典结果，因为这些函数空间在任何闭Ahlfors正则子集F∧Z上的迹是本质上定义在F上的Besov空间。我们的方法通过底层度量空间的双曲填充来定义函数空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.