About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 908216, 4 pages
http://dx.doi.org/10.1155/2014/908216
Research Article

Trudinger-Moser Embedding on the Hyperbolic Space

Department of Mathematics, Renmin University of China, Beijing 100872, China

Received 6 November 2013; Accepted 26 December 2013; Published 18 February 2014

Academic Editor: Julio Rossi

Copyright © 2014 Yunyan Yang and Xiaobao Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the hyperbolic space of dimension . By our previous work (Theorem 2.3 of (Yang (2012))), for any , there exists a constant depending only on and such that where , is the measure of the unit sphere in , and . In this note we shall improve the above mentioned inequality. Particularly, we show that, for any and any , the above mentioned inequality holds with the definition of replaced by . We solve this problem by gluing local uniform estimates.