@article{SEDP_2002-2003____A20_0, author = {Auscher, Pascal}, title = {Au-del\`a des op\'erateurs de {Calder\'on-Zygmund~~:} avanc\'ees r\'ecentes sur la th\'eorie $L^{p}$}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:20}, pages = {1--21}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2002-2003}, zbl = {1080.42010}, mrnumber = {2030715}, language = {fr}, url = {http://archive.numdam.org/item/SEDP_2002-2003____A20_0/} }
TY - JOUR AU - Auscher, Pascal TI - Au-delà des opérateurs de Calderón-Zygmund : avancées récentes sur la théorie $L^{p}$ JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:20 PY - 2002-2003 SP - 1 EP - 21 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2002-2003____A20_0/ LA - fr ID - SEDP_2002-2003____A20_0 ER -
%0 Journal Article %A Auscher, Pascal %T Au-delà des opérateurs de Calderón-Zygmund : avancées récentes sur la théorie $L^{p}$ %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:20 %D 2002-2003 %P 1-21 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2002-2003____A20_0/ %G fr %F SEDP_2002-2003____A20_0
Auscher, Pascal. Au-delà des opérateurs de Calderón-Zygmund : avancées récentes sur la théorie $L^{p}$. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Talk no. 20, 21 p. http://archive.numdam.org/item/SEDP_2002-2003____A20_0/
[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 | Zbl
[A] Auscher P., On necessary and sufficient conditions for -estimates of Riesz transforms associated to elliptic operators on : 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
[AHLMcT] Auscher P., Hofmann S., Lacey M., MIntosh A. & Tchamitchian Ph.. The solution of the Kato square root problem for second order elliptic operators on , Ann. Math. (2) 156 (2002) 633–654. | MR | Zbl
[AT1] Auscher P. & Tchamitchian P., Square root problem for divergence operators and related topics, Astérisque, 249, 1998. | Numdam | MR | Zbl
[AT2] Auscher, P. & Tchamitchian Ph., Square roots of elliptic second order divergence operators on strongly Lipschitz domains : 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 1247, 137-172, 1987. | Numdam | MR | Zbl
[BK1] Blunck S. & Kunstmann P., Calderón-Zygmund theory for non-integral operators and the functional calculus, Rev. Mat. Iberoamericana, to appear. | MR | Zbl
[BK2] Blunck S. & Kunstmann P., Weak type estimates for Riesz transforms, preprint. | MR | Zbl
[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 | Zbl
[CW] Coifman R. & Weiss G., Extensions of Hardy spaces and their use in Analysis, Bull. A.M.S. 83, (1977), 569–645. | MR | Zbl
[CD1] Coulhon T. & Duong X.T., Riesz transforms for , T.A.M.S., 351, 1151-1169, 1999. | MR | Zbl
[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 | Zbl
[DJ] David G. & Journé, J.-L. A boundedness criterion for generalized Calderón-Zygmund operators. Ann. Math., 120, 371–398, 1984. | MR | Zbl
[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 | Zbl
[DMc1] Duong X.T. & McIntosh A., The 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 | Zbl
[FS] Fefferman C. & Stein E., spaces in several variables, Acta Math., 129, 137-193, 1972. | MR | Zbl
[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
[G1] Grigor’yan A., Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Diff. Geom., 45, 33-52, 1997. | Zbl
[He] Hebisch, W., A multiplier theorem for Schrödinger operators, Coll. Math. 60/61, 659-664, 1990. | MR | Zbl
[HP] Hieber M. & Prüss, J., Heat kernels and maximal estimates for parabolic evolution equations, C.P.D.E. 2, 559-568, 2000. | Zbl
[HM] Hofmann S. & Martell J.M., bounds for Riesz transforms and square roots associated to second order elliptic operators, preprint. | MR | Zbl
[Ho] Hörmander L. Estimates for translation invariant operators in spaces, Acta Math. 104, 93-140, 1960. | MR | Zbl
[Li] Li Hong Quan, La transformation de Riesz sur les variétés coniques, J. Funct. Anal., 168, 145-238, 1999. | MR | Zbl
[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 | Zbl
[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 | Zbl
[M] Martell J. M., Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications, preprint. | MR
[SC1] Saloff-Coste L., A note on Poincaré, Sobolev and Harnack inequalities, Duke J. Math., 65, I.R.M.N., 27-38, 1992. | MR | Zbl
[SC2] Saloff-Coste L., Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat., 28, 315-331, 1990. | MR | Zbl
[St1] Stein E.M., Topics in harmonic analysis related to the Littlewood-Paley theory, Princeton U.P., 1970. | MR | Zbl
[St2] Stein E.M., Harmonic Analysis, real-variable methods, orthogonality, and oscillatory integrals, Princeton U.P., 1993. | MR | Zbl
[S] Strichartz R., Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52, 48-79, 1983. | MR | Zbl
[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 | Zbl