High order regularity for subelliptic operators on Lie groups of polynomial growth.

Título inglés	High order regularity for subelliptic operators on Lie groups of polynomial growth.
Título español	Regularidad de orden superior para operadores subelípticos en grupos de Lie de crecimiento polinómico.
Autor/es	Dungey, Nick
Organización	Sch. Math. Univ. New South Wales, Sydney, Australia
Revista	0213-2230
Publicación	2005, 21 (3): 929-996, 36 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Let G be a Lie group of polynomial volume growth, with Lie algebra g. Consider a second-order, right-invariant, subelliptic differential operator H on G, and the associated semigroup St = e-tH. We identify an ideal n' of g such that H satisfies global regularity estimates for spatial derivatives of all orders, when the derivatives are taken in the direction of n'. The regularity is expressed as L2 estimates for derivatives of the semigroup, and as Gaussian bounds for derivatives of the heat kernel. We obtain the boundedness in Lp, 1 < p < ∞, of some associated Riesz transform operators. Finally, we show that n' is the largest ideal of g for which the regularity results hold. Various algebraic characterizations of n' are given. In particular, n' = s Å n where n is the nilradical of g and s is tha largest semisimple ideal of g. Additional features of this article include an exposition of the structure theory for G in Section 2, and a concept of twisted multiplications on Lie groups which includes semidirect products in the Appendix.
Clasificación UNESCO	120220 ; 120106
Palabras clave español	Grupos de Lie ; Operadores elípticos ; Regularidad ; Transformadas de Riesz
Código MathReviews	MR2232672
Código Z-Math	Zbl 1099.22007
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