Analyse Complexe: Proceedings of the Journées Fermat - by E. Bedford, S. Bell (auth.), Eric Amar, Roger Gay, Nguyen PDF

By E. Bedford, S. Bell (auth.), Eric Amar, Roger Gay, Nguyen Van Thanh (eds.)

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Extra info for Analyse Complexe: Proceedings of the Journées Fermat - Journées SMF, held at Toulouse, May 24–27, 1983

Example text

Increase to ~' we get the desired conclusion. co b) Assume that oo ~ E PSH(~) ~ Lloc(~) and that u,(u~}C PSH(~) n Lloc(~) , u~ ~ u ; J u'I~"KI = uI~"K'i V i J E]N. ,u:)j ~ D J we have to prove that f ~d~ <_ S ~MA(u,u) and it is clear that we can assume that ~ is continuous. ) = = f ~ddCuj AddC(uj -u) + ~ ~ddCuj AddCu = = f (uj -u)ddCu. AddC~ + f ~ ddCu. AddC~ + f ~ ddCu. A ddCu-+f ~ ~A(u,u) , i -~ + co. ~j J J The fourth equality is valid since supp u - u . c K . ] The term [(sup * - u]ddCu. AddC~ K>j uK) J tends to zero since--(sup UK)* decreases to everywhere.

AT centre et de r a y o n (avec z p+q=n la m e s u r e ; v ( T , z ) > _ c > 0] associ6s ~ (p,p) T , ® de ~ Cn que si les aux nombres de L e l o n g fin e s t p o s s i b l e p o u r v u clue la d e n s i t ~ de de p l u s q u ' i l n ' y a p a s p r o p a g a t i o n d e s ® p e u t 8 t r e c h o i s i e de c l a s s e de analytique sur l'ouvert tronqu~ se p r o l o n g e n t e u x - m ~ m e s trace r , T ne peut se prolonger On v ~ r i f i e a l o r s l'extension On notera T i c i clue le p r o l o n g e m e n t ne s o i t p a s t r o p g r a n d e .

C dgsigne une constante ne d4pendant que de c~ et de 37 Les dgmonstrations sont donn6es en d6tail dane (Lemmes 1, 2 et 3 a) et b)) ; nous ne les repeoduieons pas ici. La seconde 4tape consiste h obtenie des estimations suppldmentaiees sue lee coefficients du coueant d'int4gration LEMME 2. Pour tout c ~ 0, Soit 0 =i 0 : 2 Y 0 .. dz. Adz. i,j=l 13 I J un coueant positif feem6 dane D2. posons A(0 ,c¢) = ~D2 ~ b D 2(z)cx ((911(z) + 622(z))_< +~. a) Soit (x > I. II existe C, ne d6pendant que de (1- I z212)°'-10- I~ 112)(0 11(z) o~, telle que + l0 21(Z) I ) -< C A(0 ,(x) , 2 b) I1 existe une constante absolue C> 0 telle que C A(0,1).

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