Au-delà des opérateurs de Calderón-Zygmund  : avancées récentes sur la théorie $L^p$

[Al] Alexopoulos G., An application of homogenization theory to harmonic analysis : Harnack inequalities and Riesz transforms on Lie groups of polynomial growth, Can. J. Math., 44, 4, 691-727, 1992. | MR 1178564 | Zbl 0792.22005

[A] Auscher P., On necessary and sufficient conditions for $L^p$-estimates of Riesz transforms associated to elliptic operators on ${ℝ}^n$ : a survey, en préparation.

[ACDH] Auscher P., Coulhon T., Duong X.T. & Hofmann S., Riesz transform on manifolds and heat kernel regularity, en préparation. | Numdam | Zbl 1086.58013

[AHLMcT] Auscher P., Hofmann S., Lacey M., M${}^{\mathrm{c}}$Intosh A. & Tchamitchian Ph.. The solution of the Kato square root problem for second order elliptic operators on ${ℝ}^n$, Ann. Math. (2) 156 (2002) 633–654. | MR 1933726 | Zbl 01851146

[AT1] Auscher P. & Tchamitchian P., Square root problem for divergence operators and related topics, Astérisque, 249, 1998. | MR 1651262 | Zbl 0909.35001

[AT2] Auscher, P. & Tchamitchian Ph., Square roots of elliptic second order divergence operators on strongly Lipschitz domains : $L^2$ theory, à paraître dans Journal d’Analyse Mathématique.

[B] Bakry D., Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée, in Séminaire de Probabilités XXI, Springer L.N. n${}^o$ 1247, 137-172, 1987. | Numdam | MR 941980 | Zbl 0629.58018

[BK1] Blunck S. & Kunstmann P., Calderón-Zygmund theory for non-integral operators and the $H^{\infty }$ functional calculus, Rev. Mat. Iberoamericana, to appear. | MR 2053568 | Zbl 1057.42010

[BK2] Blunck S. & Kunstmann P., Weak type $(p,p)$ estimates for Riesz transforms, preprint. | MR 2054523 | Zbl 02133474

[C] Calderón, A. P., Commutators, singular integrals on Lipschitz curves and applications, Proceedings of the I.C.M. Helsinki 1978 Acad. Sci. Fennica, Helsinki 1980, 85-96. | MR 562599 | Zbl 0429.35077

[CW] Coifman R. & Weiss G., Extensions of Hardy spaces and their use in Analysis, Bull. A.M.S. 83, (1977), 569–645. | MR 447954 | Zbl 0358.30023

[CD1] Coulhon T. & Duong X.T., Riesz transforms for $1\le p\le 2$, T.A.M.S., 351, 1151-1169, 1999. | MR 1458299 | Zbl 0973.58018

[CD2] Coulhon T. & Duong X.T., Maximal Regularity and kernel bounds : observations on a theorem by Hieber and Prüss, Adv. in Diff. Eqs 5, 343-368, 2000. | MR 1734546 | Zbl 1001.34046

[DJ] David G. & Journé, J.-L. A boundedness criterion for generalized Calderón-Zygmund operators. Ann. Math., 120, 371–398, 1984. | MR 763911 | Zbl 0567.47025

[DMc] Duong X.T. & McIntosh A., Singular integral operators with non-smooth kernels on irregular domains, Rev. Mat. Iberoamericana, 15, 2, 233-265, 1999. | MR 1715407 | Zbl 0980.42007

[DMc1] Duong X.T. & McIntosh A., The $L^p$ boundedness of Riesz transforms associated with divergence form operators, in Workshop on Analysis and Applications, Brisbane, 1997, Proceedings of the Centre for Mathematical Analysis, ANU Canberra 37 (1999), 15-25.

[DR] Duong X.T. & Robinson D., Semigroup kernels, Poisson bounds and holomorphic functional calculus, J. Funct. Anal., 142, 1, 89-128, 1996. | MR 1419418 | Zbl 0932.47013

[FS] Fefferman C. & Stein E., $H^p$ spaces in several variables, Acta Math., 129, 137-193, 1972. | MR 447953 | Zbl 0257.46078

[G] Grigor’yan A., The heat equation on non-compact Riemannian manifolds, in Russian : Matem. Sbornik, 182, 1, 55-87, 1991 ; English translation : Math. USSR Sb., 72, 1, 47-77, 1992. | Zbl 0776.58035

[G1] Grigor’yan A., Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Diff. Geom., 45, 33-52, 1997. | Zbl 0865.58042

[He] Hebisch, W., A multiplier theorem for Schrödinger operators, Coll. Math. 60/61, 659-664, 1990. | MR 1096404 | Zbl 0779.35025

[HP] Hieber M. & Prüss, J., Heat kernels and maximal $L^p-L^q$ estimates for parabolic evolution equations, C.P.D.E. 2, 559-568, 2000. | Zbl 0886.35030

[HM] Hofmann S. & Martell J.M., $L^p$ bounds for Riesz transforms and square roots associated to second order elliptic operators, preprint. | MR 2006497 | Zbl 1074.35031

[Ho] Hörmander L. Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104, 93-140, 1960. | MR 121655 | Zbl 0093.11402

[Li] Li Hong Quan, La transformation de Riesz sur les variétés coniques, J. Funct. Anal., 168, 145-238, 1999. | MR 1717835 | Zbl 0937.43004

[Lo1] Lohoué N., Comparaison des champs de vecteurs et des puissances du laplacien sur une variété riemannienne à courbure non positive, J. Funct. Anal., 61, 2, 164-201, 1985. | MR 786621 | Zbl 0605.58051

[Lo2] Lohoué N., Transformées de Riesz et fonctions de Littlewood-Paley sur les groupes non moyennables, C.R.A.S Paris, 306, I, 327-330, 1988. | MR 934611 | Zbl 0661.43002

[M] Martell J. M., Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications, preprint. | MR 2033231

[SC1] Saloff-Coste L., A note on Poincaré, Sobolev and Harnack inequalities, Duke J. Math., 65, I.R.M.N., 27-38, 1992. | MR 1150597 | Zbl 0769.58054

[SC2] Saloff-Coste L., Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat., 28, 315-331, 1990. | MR 1084020 | Zbl 0715.43009

[St1] Stein E.M., Topics in harmonic analysis related to the Littlewood-Paley theory, Princeton U.P., 1970. | MR 252961 | Zbl 0193.10502

[St2] Stein E.M., Harmonic Analysis, real-variable methods, orthogonality, and oscillatory integrals, Princeton U.P., 1993. | MR 1232192 | Zbl 0821.42001

[S] Strichartz R., Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52, 48-79, 1983. | MR 705991 | Zbl 0515.58037

[V] Verdera J., The fall of the doubling condition in harmonic analysis, à paraître dans Publicacions Matematiques.

[W] Weis L., A new approach to maximal regularity, Proc. of the 6th International Conference on evolution equations and their applications in physical and life sciences in Bad Herrenbald 1998, G. Lumer & L weis eds, Marcel Dekker 2000. | MR 1816431 | Zbl 0981.35030