Subcoercivity and subelliptic operators on Lie groups. II: The general case
type: Item
instance of: scholarly article
title: Subcoercivity and subelliptic operators on Lie groups. II: The general case
zbMATH Open document ID: 0841.43016
DOI: 10.1007/BF01071695
author: A. F. M. ter Elst
author: Derek W. Robinson
published in: Potential Analysis
publication date: 1996-07-14T00:00:00Z
review text: The paper is an extension of the authors' earlier article [Potential Anal. 3, 283-337 (1994; Zbl 0923.22005)] which was devoted to free nilpotent Lie groups. Using the Rothschild-Stein embedding theorem and a parametrix method developed in Section 2 the authors extend their previous results to general Lie groups and their representations. They derive a number of regularity properties of Lie group representations and obtain the boundedness and smoothness results for the semigroup kernel corresponding to a subcoercive operator and a general Lie group. In particular, for a second-order operator with complex coefficients the equivalence of subcoercivity and subellipticity is proved.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 763779
zbMATH Keywords: free nilpotent Lie groups
zbMATH Keywords: Rothschild-Stein embedding theorem
zbMATH Keywords: representations
zbMATH Keywords: semigroup
zbMATH Keywords: kernel
zbMATH Keywords: subcoercivity
zbMATH Keywords: subellipticity
Wikidata QID: Q115394439
reviewed by: Yuri I. Karlovich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 763779