Geometric characterizations of embedding theorems
Classical Analysis and ODEs
2016-01-25 v1 Functional Analysis
Abstract
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type in the sense of Coifman and Weiss. We prove that embedding theorems hold on spaces of homogeneous type if and only if geometric conditions, namely the measures of all balls have lower bounds, hold. As applications, our results provide new and sharp previous related embedding theorems for the Sobolev, Besov and Triebel-Lizorkin spaces.
Cite
@article{arxiv.1601.06125,
title = {Geometric characterizations of embedding theorems},
author = {Yanchang Han and Yongsheng Han and Ji Li},
journal= {arXiv preprint arXiv:1601.06125},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1507.07187