Sharp constants for weighted Moser-Trudinger inequalities on groups of Heisenberg type

详细信息    查看全文

• 作者：Nguyen Lam ; Hanli Tang
• 关键词：Moser&ndash ; Trudinger inequalities ; Weights ; Sharp constants ; Groups of Heisenberg type
• 刊名：Nonlinear Analysis
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：89
• 期：Complete
• 页码：95-109
• 全文大小：435 K

文摘

Let be a group of Heisenberg type, be its homogeneous dimension, , . For , we write , where is the coordinate of corresponding to the center of the Lie algebra of , is corresponding to the orthogonal complement of . Let be the homogeneous norm of , be a weight. The main purpose of this paper is to establish sharp constants for weighted Moser-Trudinger inequalities on domains of finite measure in () and on unbounded domains (). We also establish the weighted inequalities of Adachi-Tanaka type on the entire (). Our results extend the sharp Moser-Trudinger inequalities on domains of finite measure in Cohn and Lu (2001, 2002) and on unbounded domains in Lam et?al. (2012) to the weighted case and improve the sharp weighted Moser-Trudinger inequality proved in Tyson (2006) on domains of finite measure on . The usual symmetrization method (i.e., rearrangement argument) is not available on such groups and therefore our argument is a rearrangement-free argument recently developed in Lam and Lu (2012)? . Our weighted Adachi-Tanaka type inequalities extend the nonweighted results in Lam et?al. (2012)? .