Author : John M. Maki
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (774 download)
Book Synopsis Analysis in the Heisenberg Group: Weak S-John Domains and the Dimensions of Graphs of Holder Functions by : John M. Maki
Download or read book Analysis in the Heisenberg Group: Weak S-John Domains and the Dimensions of Graphs of Holder Functions written by John M. Maki and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we provide connections between analytic properties in Euclidean R^n and analytic properties in sub-Riemannian Carnot groups. We introduce weak s-John domains, in analogy with weak John domains, and we prove that weak s-John is equivalent to a localized version. This is applied in showing that a bounded C^{1,alpha} domain in R^3 will be a weak s-John domain in the first Heisenberg group. This result is sharp, giving a precise value of s that depends only on alpha. We follow upon this by showing that a weak s-John domain in a general Carnot group will be a (q,p)-Poincare domain for certain p and q that depend only on s and the homogeneous dimension of the Carnot group. The final result gives, in a general Carnot group, an upper bound on the lower box dimension of the graph of an Euclidean Holder function, with application to the dimension of a Sobolev graph.