This is a preview of subscription content, log in via an institution to check access.
References
[B] Bony, J.M.: Principle du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opèrateurs elliptiques dégénérés. Ann. Inst. Fourier (Grenoble)19 (1), 277–304 (1969)
[B-R] Birgé, L., Raugi, A.: Fonctions harmoniques sur les groupes moyennables, C.R. Acad. Sci. Paris278, 1287–1289 (1974)
[D1] Damek, E.: Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups. Studia Math.89, 169–196 (1988)
[D2] Damek, E.: Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group, Studia Math. To appear
[D-H] Damek, E., Hulanicki, A.: Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group, Studia Math.101 (1), 33–68 (1991)
[F-K-P] Fefferman, R.A., Kenig, C.E., Pipher, J., The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math.134, 65–124 (1991).
[F-S] Folland, G.B., Stein, E.: Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982
[H] Hörmander, L.: Estimates for translation invariant operators inL p spaces, Acta Math.104, 93–140 (1960)
[H1] Hulanicki, A.: Subalgebra ofL 1(G) associated with Laplacian on a Lie group. Colloq. Math.31, 259–287 (1974)
[H2] Hulanicki, A.: Maximal functions at infinity for Poisson integrals on NA in Harmonic Analysis and Discrete Potential Theory, Plenum Press, New York and London, 15–22
[H-J] Hulanicki, A., Jenkins, J.: Nilpotent groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math.80, 235–244 (1984)
[K] Krantz, S.G.: Invariant Metric and the Boundary Behavior of Holomorphic Functions on Domains in ℂn, The Journal of Geometric Analysis,1 (2), 71–97 (1991)
[Ko] Korányi, A.: Harmonic functions on symmetric spaces, in Symmetric Spaces, Basel-New York 1972
[S-S] Saloff-Coste, L., Stroock, D.W.: Opérateurs uniformément sous-elliptiques sur les groupes de Lie, Jour. Func. Analysis98 (1), 97–121 (1991)
[S] Stroock, D.: Lectures on Stochastic Analysis: Diffusion Theory, Cambridge Univ. Press, 1987
[St] Stein, E. M.: Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals, Invent. Math.74, 63–83 (1983)
[S-W] Stein E.M., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press 1971
[V-S-C] Varopoulos, N., Saloff-Coste, L., Coulhon, T.: Analysis and Geometry on Groups, Cambridge Univ. Press 1992
[Z] Zienkiewicz, J.: Maximal estimates for nonsymmetric semigroups studia Math.109 (1), 41–49 (1994)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Damek, E. Maximal functions related to subelliptic operators with polynomially growing coefficients. Math Z 218, 349–374 (1995). https://doi.org/10.1007/BF02571909
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571909