Let $X_0, X_1,..., X_k$ be left-invariant vector fields on a Lie group and let $L = ∑_{i=1}^k X_i^2 + X_0$. Then L is the infinitesimal generator of a semigroup ${p_t}_{t≥0}$ of probability measures on G. Let $P*f(x) = ∑_{0
Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
[CW] R. Coifman et G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, New York, 1971.
[Co] M. Cowling, G. Gaudry, S. Giulini and G. Mauceri, Weak type (1,1) estimates for heat kernel maximal functions on Lie groups, Trans. Amer. Math. Soc. 323 (1991), 637-649.
[DH] E. Damek and A. Hulanicki, Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group, Studia Math. 101 (1991), 33-68.
[FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982.
[G] Y. Guivarc'h, Sur la loi des grands nombres et le rayon spectral d'une marche aléatoire, Astérisque 74 (1980), 47-98.
[He] W. Hebisch, Estimates on the semigroups generated by left invariant operators on Lie groups, J. Reine Angew. Math. 423 (1992), 1-45.
[Hö] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171.
[S] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Princeton Univ. Press, 1970.
[V] N. Th. Varopoulos, Analysis on Lie groups, J. Funct. Anal. 76 (1988), 346-410.
[Y] K. Yosida, Functional Analysis, Springer, 1965.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv109i1p41bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.