Sur l'existence de solutionsC 1, 1/n,C 1, 1 etC 2, radiales pour des équations de type Monge-Ampère complexe dans la boule unité de ℂ n

Sans résumé     

Local analyticity for the [`(?)]\overline \partial -Neumann problem in completely decoupled pseudoconvex domains-Neumann problem in completely decoupled pseudoconvex domains

In this paper we prove local analyticity of solutions to the -Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These are domains that are locally of the form Imw > Σ |h _k (z _k )|² with eachh _k holomorphic and vanishing only at 0. As in those earlier papers, we use purelyL ² methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew.     

Sur l'inégalité de Poincaré, à support compact, pour un ou plusieurs champs de vecteurs

Nous démontrons, dans cette note, une inégalité de type Poincaré pour un ou plusieurs champs de vecteurs , et des fonctions régulières à support contenu dans un voisinage d'une hypersurface , sous une hypothèse naturelle de contact entre et la famille . La constante intervenant dans cette inégalité est précisément reliée à l'épaisseur du voisinage autour de et à l'ordre du contact entre et .

     

Inégalités à priori et estimation sous-elliptique pour\bar \partial dans des ouverts non pseudoconvexes

Sans résumé     

Direct arylation of oxazole and benzoxazole with aryl or heteroaryl halides using a palladium-diphosphine catalyst

Through the use of PdCl(dppb)(C₃H₅) as a catalyst, a range of aryl bromides and chlorides undergoes coupling via C-H bond activation/functionalization reaction with oxazole or benzoxazole in good yields. This air-stable catalyst can be used at low loadings with several substrates. Surprisingly, better results in terms of substrate/catalyst ratio were obtained in several cases using electron-excessive aryl bromides than with the electron-deficient ones. This seems to be mainly due to the relatively low thermal stability of some of the 2-arylbenzoxazoles formed with electron-deficient aryl halides. With these substrates, in order to obtain higher yields of product, the reactions had to be performed at a lower temperature (100-120 °C) using a larger amount of catalyst. On the other hand, in the presence of the most stable products, the reactions were performed at 150 °C using as little as 0.2 mol% catalyst. Arylation of benzoxazole with heteroaryl bromides also gave the coupling products in moderate to high yields using 0.2-5 mol% catalyst. With this catalyst, electron-deficient aryl chloride such as 4-chlorobenzonitrile, 4-chloroacetophenone or 2-chloronitrobenzene have also been used successfully.     

Palladium-catalyzed direct heteroarylation of chloropyridines and chloroquinolines

The direct coupling of aryl chlorides with heteroarenes would be a considerable advantage for sustainable development due to their lower cost, lower mass, the wider diversity of available compounds and also because of the formation of only HCl associated to a base as by-product and the reduction of the number of steps to prepare these compounds. We observed that through the use of PdCl(dppb)(C₃H₅) as a catalyst, a range of heteroaryl derivatives undergoes coupling via C-H bond activation/functionalization reaction with chloropyridines or chloroquinolines in low to high yields. This air-stable catalyst can be used with a wide variety of substrates. The position of the chloro substituent on pyridines has a minor influence on the yields. On the other hand, the nature on the heteroaryl derivative has a large influence. The highest yields were obtained using benzoxazole, thiophene or thiazole derivatives. The coupling of chloropyridines with furans also gave the expected products, but in low to moderate yields.     

Le principe de reflexion en des points de faible pseudo convexite,pour des applications holomorphes propres

Sans résumé     

Microlocalisation et estimations pour\bar \partial _b dans quelques hypersurfaces pseudoconvexes

Résume Nous étudions des estimations précises pour sur des hypersurfaces dont la matrice de Levi dans une base a une certaine forme. En particulier, nous donnons, par la méthode de microlocalisation, une démonstration très simple des estimations dites maximales lorsque les valeurs propres sont comparables. Nous obtenons en fait une précision supplémentaire (inégalité 3.17) qui permet de considérer des cas plus généraux. Finalement, de telles estimations, on déduit des estimations sous elliptiques optimales pour .

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Summary We study precise estimates for on hypersurfaces the Levi matrix of which has certain form. In particular, we give and simple proof of the so-called maximal estimates, using the microlocal analysis. In fact, we obtain a refined version (inequality 3.17), which permits the study of more general cases. Finally, from such estimates, we deduce optimal subelliptic estimates for .

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Oblatum 3-IX-1990