An estimate for a first-order riesz operator on the affine group

Transactions of the American Mathematical Society

Volumn 351, Issue 8, 1999, Pages 3301-3314

  Sjögren, Peter ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644451967     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-99-02222-9     Document Type: Article

References (21)

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. MR 93j:22006
2. J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297. MR 93b:43007
3. D. Bakry, Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée. In Séminaire de Probabilité XXI, J. Azéma et al. (eds), Lecture Notes in Mathematics 1247, Springer-Verlag 1987, 137-172. MR 89h:58208
4. M.S. Birman and M.Z. Solomjak, Spectral theory of self-adjoint operators in Hilbert space. (Mathematics and its applications (Soviet series) Reidel, Dordrecht 1987. MR 93g:47001
5. p-regularity of subelliptic operators on Lie groups. J. Operator Theory 31 (1994), 165-187. MR 96a:22013
6. Th. Coulhon and X.Th. Duong, Riesz transforms for 1 ≤ p ≤ 2. To appear in Trans. Amer. Math. Soc. CMP 97:15
7. R.E. Edwards and G.I. Gaudry, Littlewood-Paley and multiplier theory. Ergebnisse der Mathematik und ihrer Grenzgebiete 90, Springer-Verlag, Berlin Heidelberg New York 1977. MR 58:29760
8. G.I. Gaudry, T. Qian and P. Sjögren, Singular integrals related to the Laplacian on the affine group ax + b. Ark. Mat. 30 (1992), 259-281.
9. G. Gaudry and P. Sjögren, Singular integrals on Iwasawa NA groups of rank 1. J. Reine Angew. Math. 479 (1996), 39-66. MR 97k:22012
10. G. Gaudry and P. Sjögren, Singular integrals on the complex affine group. Coll. Math. 75 (1998), 133-148. CMP 98:06
11. G. Gaudry and P. Sjögren, Haar-like expansions and boundedness of a Riesz operator on a solvable group. To appear in Math. Zeitschr.
12. A. Hulanicki, On the spectrum of the Laplacian on the affine group of the real line. Studia Math. 54 (1976), 199-204. MR 53:3195
13. N. Lohoué, Comparaison des champs de vecteurs et des puissances du laplacien sur une variétés riemanniennes à courbure non positive. J. Funct. Anal. 61 (1985), 164-201. MR 86k:58117
14. 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. MR 89b:43008
15. 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. MR 87b:43008
16. W. Magnus and F. Oberhettinger, Formulas and theorems for the special functions of math- ematical physics. Chelsea Publishing Company, New York 1949. MR 10:532b
17. L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynômiale. Ark. Mat. 28 (1990), 315-331. MR 92d:22014
18. E.M. Stein, Singular integrals and differentiability properties of functions. Princeton University Press, Princeton 1970. MR 44:7280
19. E.M. Stein and N.J. Weiss, On the convergence of Poisson integrals. Trans. Amer. Math. Soc. 140 (1969), 35-54. MR 39:3024
20. J.-O. Strömberg, Weak type L1 estimates for maximal functions on non-compact symmetric spaces and biinvariant convolutions. Unpublished manuscript, 1979.
21. J.-O. Strömberg, Weak type L1 estimates for maximal functions on non-compact symmetric spaces. Ann. Math. 114 (1981), 115-126. MR 82k:43010