Subcoercivity and subelliptic operators on Lie groups. II: The general case (Q1891642)

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.