Riesz transform on manifolds and Poincaré inequalitie

 Access to full text

 Full (PDF)

1. [1] P. Auscher, On $L^p$-estimates for square roots of second order elliptic operators on ${ℝ}^n$, Publ. Mat. 48 (2004), 159-186. Zbl1107.42003MR2044643
2. [2] P. Auscher, T. Coulhon, X. T. Duong and S. Hofmann, Riesz transforms on manifolds and heat kernel regularity, Ann. Sci. École Norm. Sup. 37 (2004), 911-95. Zbl1086.58013MR2119242
3. [3] P. Auscher and J.-M. Martell, Weighted norm inequalities off-diagonal estimates and elliptic operators: Part I, preprint 2005. MR2664561
4. [4] P. Auscher and P. Tchamitchian, “Square Root Problem for Divergence Operators and Related Topics”, Astérisque, 249, 1998. Zbl0909.35001MR1651262
5. [5] D. Bakry, Transformations de Riesz pour les semi-groupes symétriques, Seconde partie: étude sous la condition ${\Gamma }_2\ge 0$, In: “Séminaire de Probabilités XIX”, Lect. Notes Math., Vol. 1123, Springer-Verlag, 1985, 145–174. Zbl0561.42011MR889473
6. [6] S. Blunck and P. Kunstmann, Calderón-Zygmund theory for non-integral operators and the $H^{\infty }$ functional calculus, Rev. Mat. Iberoamericana 19 (2003), 919–942. Zbl1057.42010MR2053568
7. [7] G. Carron, T. Coulhon and A. Hassell, Riesz transform and $L^p$ cohomology for manifolds with Euclidean ends, Duke Math. J., to appear. Zbl1106.58021MR2219270
8. [8] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645. Zbl0358.30023MR447954
9. [9] T. Coulhon and X. T. Duong, Riesz transforms for $1\le p\le 2$, Trans. Amer. Math. Soc. 351 (1999), 1151–1169. Zbl0973.58018MR1458299
10. [10] T. Coulhon and X. T. Duong, Riesz transform and related inequalities on non-compact Riemannian manifolds, Comm. Pure Appl. Math. 56, 12 (2003), 1728–1751. Zbl1037.58017MR2001444
11. [11] T. Coulhon and H. Q. Li, Estimations inférieures du noyau de la chaleur sur les variétés coniques et transformée de Riesz, Arch. Math. 83 (2004), 229–242. Zbl1076.58017MR2108551
12. [12] B. Franchi, C. Pérez and R. Wheeden, Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type, J. Funct. Anal. 153 (1998), 108–146. Zbl0892.43005MR1609261
13. [13] F. W. Gehring, The $L^p$-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277. Zbl0258.30021MR402038
14. [14] M. Giaquinta, “Multiple Integrals in the Calculus of Variations and Non-linear Elliptic Systems”, Annals of Math. Studies, vol. 105, Princeton Univ. Press, 1983. Zbl0516.49003MR717034
15. [15] A. Grigor’yan, Stochastically complete manifolds, (Russian) Dokl. Akad. Nauk SSSR 290 (1986), 534–537. Zbl0632.58041MR860324
16. [16] A. Grigor’yan, Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold, J. Funct. Anal. 127 (1995), 363–389. Zbl0842.58070MR1317722
17. [17] A. Grigor’yan and L. Saloff-Coste, Stability results for Harnack inequalities, Ann. Inst. Fourier (Grenoble) 55 (2005), 825–890. Zbl1115.58024MR2149405
18. [18] P. Hajłasz and P. Koskela, “Sobolev Met Poincaré”, Mem. Amer. Math. Soc., Vol. 145, no. 688, 2000. Zbl0954.46022MR1683160
19. [19] S. Hofmann and J.-M. Martell, $L^p$ bounds for Riesz transforms and square roots associated to second order elliptic operators, Publ. Mat. 47 (2003), 497–515. Zbl1074.35031MR2006497
20. [20] T. Iwaniec, The Gehring lemma, In: “Quasiconformal Mappings and Analysis” (Ann. Arbor, MI, 1995), Springer, New York, 1998, 181–204. Zbl0888.30017MR1488451
21. [21] S. Keith and X. Zhong, The Poincaré inequality is an open ended condition, preprint 2003. Zbl1180.46025MR2415381
22. [22] Li Hong-Quan, La transformation de Riesz sur les variétés coniques, J. Funct. Anal. 168 (1999), 145–238. Zbl0937.43004MR1717835
23. [23] J.-M. Martell, PhD thesis, Universidad Autónoma de Madrid, 2003. 
24. [24] N. G. Meyers, An $L^p$ estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 17 (1963), 189–206. Zbl0127.31904MR159110
25. [25] L. Saloff-Coste, A note on Poincaré, Sobolev and Harnack inequalities, Internat. Math. Res. Notices 2 (1992), 27–38. Zbl0769.58054MR1150597
26. [26] L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Anal. (4), 4 (1995), 429–467. Zbl0840.31006MR1354894
27. [27] Z. Shen, Bounds of Riesz transforms on $L^p$ spaces for second order elliptic operators, Ann. Inst. Fourier (Grenoble) 55 (2005), 173-197. Zbl1068.47058MR2141694
28. [28] E. M. Stein, “Singular Integrals and Differentiability Properties of Functions”, Princeton Univ. Press, 1970. Zbl0207.13501MR290095
29. [29] E. M. Stein, “Topics in Harmonic Analysis Related to the Littlewood-Paley Theory”, Princeton Univ. Press, 1970. Zbl0193.10502MR252961

1. Peter Sjögren, Maria Vallarino, Boundedness from $H^1$ to $L^1$ of Riesz transforms on a Lie group of exponential growth
2. Steve Hofmann, Svitlana Mayboroda, Alan McIntosh, Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces
3. Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann, Riesz transform on manifolds and heat kernel regularity