Estimates for the poisson kernels and their derivatives on rank one N A groups

Studia Mathematica

Volumn 126, Issue 2, 1997, Pages 115-148

  Damek, Ewa ^a   Hulanicki, Andrzej ^a   Zienkiewicz, Jacek ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013297161     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. A. Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary, Ann. of Math. 125 (1987), 495-535.
2. M. Babillot, Théorie de renouvellement pour des chaînes semi-markoviennes transientes, Ann. Inst. H. Poincaré 24 (1988), 507-569.
3. n in the critical case, Ann. Probab. 25 (1997), 478-493.
4. L. Birgé et A. Raugi, Fonctions harmoniques sur les groupes moyennables, C. R. Acad. Sci. Paris 278 (1974), 1287-1289.
5. E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-195.
6. _, Pointwise estimates for the Poisson kernel on N A groups by the Ancona method, Ann. Fac. Sci. Toulouse 5 (1996), 421-441.
7. _, Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms, Colloq. Math. 73 (1997), 229-249.
8. E. Damek and A. Hulanicki, Boundaries for left-invariant subelliptic operators on semidirect products of nilpotent and abelian groups, J. Reine Angew. Math. 411 (1990), 1-38.
9. E. Damek and A. Hulanicki, Maximal functions related to subelliptic operators invariant under the action of a solvable group, Studia Math. 101 (1991), 33-68.
10. _, _, Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups, Colloq. Math. 68 (1995), 121-140.
11. E. Damek and F. Ricci, Harmonic analysis on solvable extensions of H-type groups, J. Geom. Anal. 2 (1992), 213-249.
12. E. Heintze, On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974), 23-34.
13. 1(G) associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
14. P. Malliavin, Géometrie Différentielle Stochastique, Sém. Math. Sup. 64, Les Presses de l'Université de Montréal, Montréal, 1977.
15. E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615.
16. n, Uspekhi Mat. Nauk 20 (2) (1965), 3-51 (in Russian); English transl.: Russian Math. Surveys 20 (1966), 1-48.
17. n, Uspekhi Mat. Nauk 20 (2) (1965), 3-51 (in Russian); English transl.: Russian Math. Surveys 20 (1966), 1-48.
18. A. Raugi, Fonctions harmoniques sur les groupes localement compacts à base dénombrable, Bull. Soc. Math. France Mém. 54 (1977), 5-118.
19. D. W. Robinson, Elliptic Operators and Lie Groups, Oxford Math. Monographs, Clarendon Press, 1991.
20. J. Solowiej, Fatou theorem-a negative result, Colloq. Math. 67 (1995), 131-145.
21. D. Stroock, Lectures on Stochastic Analysis: Diffusion Theory, Cambridge Univ. Press, 1987.
22. D. Stroock and S. R. Varadhan, Multidimensional Diffusion Processes, Springer, 1979.
23. J. C. Taylor, Skew products, regular conditional probabilities and stochastic differential equations: a technical remark, in: Séminaire de Probabilités XXVI, Lecture Notes in Math. 1526, Springer, 1992, 113-126.
24. K. Urbanik, Functionals of transient stochastic processes with independent increments, Studia Math. 103 (1992), 299-314.
25. N. T. Varopoulos, Diffusion on Lie groups (I), Canad. J. Math. 46 (1994), 1073-1093.
26. _, The heat kernel on Lie groups, Rev. Mat. Iberoamericana 12 (1996), 147-186.
27. N. T. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and Geometry on Groups, Cambridge Tracts in Math. 100, Cambridge Univ. Press, 1992.
28. E. B. Vinberg, The theory of convex homogeneous cones, Trans. Moscow Math. Soc. 12 (1963), 340-403.