Haar-like expansions and boundedness of a Riesz operator on a solvable Lie group

Mathematische Zeitschrift

Volumn 232, Issue 2, 1999, Pages 241-256

  Gaudry, Garth ^a   Sjögren, Peter ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040715721     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002090050512     Document Type: Article

References (16)

1. G. Alexopoulos, An application of homogenization theory to harmonic analysis: Harnack inequalities and Riesz transforms on Lie groups of polynomial growth. Can. J. Math. 44 (1992), 691-727.
2. J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297.
3. D. Bakry, Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée. In Séminaire de Probabilités XXI, J. Azéma et al. (eds), Lecture Notes in Mathematics 1247, Springer-Verlag 1987, 137-172.
4. p-regularity of subelliptic operators on Lie groups. J. Operator Theory 31 (1994), 165-187.
5. Th. Coulhon and X.T. Duong, Riesz transforms for 1 < p < 2. To appear in Trans. Amer. Math. Soc.
6. G.I. Gaudry, T. Qian and P. Sjögren, Singular integrals related to the Laplacian on the affine group aχ + b. Ark. Mat. 30 (1992), 259-281.
7. G. Gaudry and P. Sjögren, Singular integrals on Iwasawa N A groups of rank 1. J. reine angew. Math. 479 (1996), 39-66.
8. G. Gaudry and P. Sjögren, Singular integrals on the complex affine group. Coll. Math. 75(1998), 133-148.
9. N. Lohoué, Comparaison des champs de vecteurs et du laplacien sur les variétés riemanniennes à courbure non positive. J. Funct. Anal. 61 (1985), 164-201.
10. N. Lohoué, Transformées de Riesz et fonctions de Littlewood-Paley sur les groupes non moyennables. C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), 327-330.
11. N. Lohoué and N.Th. Varopoulos, Remarques sur les transformées de Riesz sur les groupes de Lie nilpotents. C. R. Acad. Sci. Sér. I Math. 301 (1985), 559-560.
12. W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and theorems for the special functions of mathematical physics. 3rd Edition, Springer-Verlag, Berlin·Heidelberg·New York, 1966.
13. L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynômiale. Ark. Mat. 28 (1990), 315-331.
14. P. Sjögren, An estimate for a first-order Riesz operator on the affine group. To appear in Trans. Amer. Math. Soc.
15. E.M. Stein, Boundary behavior of harmonic functions on symmetric spaces: Maximal estimates for Poisson integrals. Invent. Math. 74 (1983), 63-83.
16. M. Wängefors, An estimate for some first-order Riesz operators on Iwasawa N A groups of rank 1. Preprint, 1997.