H1-L1 Boundedness of Riesz Transforms on Riemannian Manifolds and on Graphs

Potential Analysis

Volumn 14, Issue 3, 2001, Pages 301-330

  Russ, Emmanuel ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

H1at; Heat kernel; H rmander integral condition; Markov kernel; Riesz transforms

Indexed keywords

EID: 0035611894     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011269629655     Document Type: Article

References (15)

1. Auscher, P. and Tchamitchian, P.: Square Root Problem for Divergence Operators and Related Topics, Astérisque 249, 1998.
2. Bakry, D.: 'Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée', in Séminaire de Probabilités XXI, Lecture Notes in Math. 1247, 1987, pp. 137-172.
3. Bakry, D.: 'La propriété de sous-harmonicité des diffusions dans les variétés', in Séminaire de Probabilités XXII, Lecture Notes in Math. 1321, 1989, pp. 1-50.
4. 1 and B M O on Positively Curved Manifolds and Their Characterization, in Lecture Notes in Math. 1494, Springer-Verlag, 1991, pp. 23-38.
5. Coifman, R. and Weiss, G.: 'Extensions of Hardy spaces and their use in analysis', Bull. Amer. Math. Soc. 83(4) (1977), 569-645.
6. Coulhon, T. and Duong, X. T.: 'Riesz transforms for 1 ≤ p ≤ 2', Trans. Amer. Math. Soc. 354(3) (1999), 1151-1169.
7. Coulhon, T. and Saloff-Coste, L.: 'Variétés riemanniennes isométriques à l'infini', Rev. Mat. Iberoamericana 11(3) (1995).
8. Delmotte, T.: 'Parabolic Harnack inequality and estimates of Markov chains on graphs', Rev. Mat. Iberoamericana 15(1) (1999), 181-232.
9. Grigor'yan, A.: 'Integral maximum principle and its applications', Proc. Royal Soc. Edinburgh Sect. A 124 (1994), 353-362.
10. Grigor'yan, A.: 'Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold', J. Funct. Anal. 127 (1995), 363-389.
11. 1-B M O duality on graphs, Preprint.
12. 1-B M O duality on Riemannian manifolds, Preprint.
13. Russ, E.: 'Riesz transforms on graphs for 1 ≤ p ≤ 2', to appear in Math. Scand. 14. Saloff-Coste, L.: 'Parabolic Harnack inequality for divergence form second order differential operators', Potential Anal. 4(4) (1995), 429-467.
14. Russ, E.: 'Riesz transforms on graphs for 1 ≤ p ≤ 2', to appear in Math. Scand. 14. Saloff-Coste, L.: 'Parabolic Harnack inequality for divergence form second order differential operators', Potential Anal. 4(4) (1995), 429-467.
15. Stein, E. M.: Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.