{"title":"Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces","authors":"S. Hofmann, S. Mayboroda, A. Mcintosh","doi":"10.24033/ASENS.2154","DOIUrl":"https://doi.org/10.24033/ASENS.2154","url":null,"abstract":"Let L be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with L, such as the heat semigroup and Riesz transform, are not, in general, of CalderonZygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in Lp, Sobolev, and some new Hardy spaces naturally associated to L. First, we show that the known ranges of boundedness in Lp for the heat semigroup and Riesz transform of L, are sharp. In particular, the heat semigroup e−tL need not be bounded in Lp if p < [2n/(n+2), 2n/(n−2)]. Then we provide a complete description of all Sobolev spaces in which L admits a bounded functional calculus, in particular, where e−tL is bounded. Secondly, we develop a comprehensive theory of Hardy and Lipschitz spaces associated to L, that serves the range of p beyond [2n/(n + 2), 2n/(n − 2)]. It includes, in particular, characterizations by the sharp maximal function and the Riesz transform (for certain ranges of p), as well as the molecular decomposition and duality and interpolation theorems.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"29 1","pages":"723-800"},"PeriodicalIF":1.9,"publicationDate":"2010-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82700795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale","authors":"C. G. Moreira, J. Yoccoz","doi":"10.24033/ASENS.2115","DOIUrl":"https://doi.org/10.24033/ASENS.2115","url":null,"abstract":"Soit F o un diffeomorphisme d'une surface possedant deux fers a cheval A, A' tels que W s Λ et W u Λ' aient en un point q une tangence quadratique isolee. Nous montrons que, si la somme des dimensions transverses de W s Λ et W\"A' est strictement plus grande que 1, les diffeomorphismes voisins de F o tels que W s Λ et W u Λ' soient stablement tangents au voisinage de q forment une partie de densite inferieure strictement positive en F 0 .","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"56 1","pages":"1-68"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72826819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation","authors":"Eric Lombardi, L. Stolovitch","doi":"10.24033/ASENS.2131","DOIUrl":"https://doi.org/10.24033/ASENS.2131","url":null,"abstract":"Dans cet article, nous etudions des germes de champs de vecteurs holomorphes qui sont des perturbations « d'ordres superieurs » de champs de vecteurs quasi-homogenes au voisinage de l'origine de ℂ n , point fixe des champs consideres. Nous definissons une condition « diophantienne » sur le champ quasi-homogene initial S qui assure que si une telle perturbation de S est formellement conjuguee a S alors elle l'est aussi holomorphiquement. Nous etudions le probleme de mise sous forme normale relativement a S. Nous donnons une condition suffisante assurant l'existence d'une transfor- mation holomorphe vers une forme normale. Lorsque cette condition n'est pas satisfaite, nous mon- trons neanmoins, sous une condition raisonnable, l'existence d'une normalisation formelle Gevrey vers une forme normale Gevrey. Enfin, nous montrons l'existence d'une approximation exponentiellement bonne de la dynamique par une forme normale partielle.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"69 1","pages":"659-718"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89513906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DIASTOLIC AND ISOPERIMETRIC INEQUALITIES ON SURFACES","authors":"F. Balacheff, S. Sabourau","doi":"10.24033/ASENS.2128","DOIUrl":"https://doi.org/10.24033/ASENS.2128","url":null,"abstract":"Nous demontrons une inegalite universelle entre la diastole, definie par un procede de minimax sur l'espace des 1-cycles, et l'aire d'une surface riemannienne fermee. De maniere informelle, nous prouvons que toute surface riemannienne fermee peut etre balayee par une famille de multi-lacets dont les longueurs sont controlees par l'aire de la surface. Cette inegalite diastolique, qui repose sur une majoration de la constante de Cheeger, fournit en particulier un procede effectif pour trouver de courtes geodesiques fermees sur une 2-sphere. Nous deduisons que toute surface riemannienne peut etre decomposee en deux domaines de meme aire dont la longueur du bord commun est majoree a l'aide de l'aire de la surface. Nous comparons egalement divers invariants riemanniens sur la 2-sphere afin de souligner le role special joue par la diastole.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"15 1","pages":"579-605"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85032654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regularity analysis for systems of reaction-diffusion equations","authors":"T. Goudon, A. Vasseur","doi":"10.24033/ASENS.2117","DOIUrl":"https://doi.org/10.24033/ASENS.2117","url":null,"abstract":"Ce travail est consacre a l'etude de la regularite des solutions de certains systemes d'equations de reaction-diffusion. En particulier, nous montrons que les solutions peuvent etre bornees et regulieres en dimensions un et deux alors qu'en dimensions superieures nous discutons la dimension de Hausdorff de l'ensemble des points singuliers. L'approche proposee ici s'inspire de la methode de De Giorgi pour etudier la regularite de problemes elliptiques avec des coefficients discontinus. La preuve exploite la stucture specifique des systemes consideres et n'est pas une simple adaptation de techniques scalaires. L'entropie associee naturellement au systeme joue un role crucial dans cette analyse.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"116 1","pages":"117-142"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87766835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE CUBIC SZEGÖ EQUATION","authors":"P. Gérard, S. Grellier","doi":"10.24033/ASENS.2133","DOIUrl":"https://doi.org/10.24033/ASENS.2133","url":null,"abstract":"On considere l'equation hamiltonienne suivante sur l'espace de Hardy du cercle i∂ t u = Π(|u| 2 u), ou II designe le projecteur de Szego. Cette equation est un cas modele d'equation sans aucune propriete dispersive. On etablit qu'elle admet une paire de Lax et une infinite de lois de conservation en involution, et qu'elle peut etre approchee par une suite de systemes hamiltoniens de dimension finie completement integrables. Neanmoins, on met en evidence des phenomenes d'instabilite illustrant la degenerescence de cette structure completement integrable. Enfin, on caracterise les ondes progressives de ce systeme.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"32 1","pages":"761-810"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88773608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"HODGE-TATE AND DE RHAM REPRESENTATIONS IN THE IMPERFECT RESIDUE FIELD CASE","authors":"K. Morita","doi":"10.24033/ASENS.2122","DOIUrl":"https://doi.org/10.24033/ASENS.2122","url":null,"abstract":"Soit K un corps local p-adique de corps residuel k tel que [k: k P ] = p e < +∞ et soit V une representation p-adique de Gal(K/K). Nous utilisons la theorie des modules differentiels p-adiques pour montrer que V est une representation de Hodge-Tate (resp. de Rham) de Gal(K/K) si et seulement si V est une representation de Hodge-Tate (resp. de Rham) de Gal(k pf /k pf ) ou K pf /K est un certain corps local p-adique de corps residuel le plus petit corps parfait k pf contenant k.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"6 1","pages":"341-355"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86218634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$mathrm {B}_{mathrm {dR}}$-représentations dans le cas relatif","authors":"Fabrizio Andreatta, Olivier Brinon","doi":"10.24033/ASENS.2121","DOIUrl":"https://doi.org/10.24033/ASENS.2121","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"1 1","pages":"279-339"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88689109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the asymptotic geometry of gravitational instantons","authors":"V. Minerbe","doi":"10.24033/ASENS.2135","DOIUrl":"https://doi.org/10.24033/ASENS.2135","url":null,"abstract":"We investigate the geometry at infinity of the so-called \"gravitational instan- tons\", i.e. asymptotically flat hyperkahler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"1 1","pages":"883-924"},"PeriodicalIF":1.9,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82328594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derived invariance of the number of holomorphic $1$-forms and vector fields","authors":"M. Popa, C. Schnell","doi":"10.24033/ASENS.2149","DOIUrl":"https://doi.org/10.24033/ASENS.2149","url":null,"abstract":"NOTICE: this is the author’s version of a work that was accepted for publication in Annales Scientifiques de l'Ecole Normale Superieure . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annales Scientifiques De l Ecole Normale Superieure, [Vol 44, Issue 3, May-June 2011] The original publication is available at www.elsevier.com.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"103 1","pages":"527-536"},"PeriodicalIF":1.9,"publicationDate":"2009-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80785708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}