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

ISBN-10: 3540138862

ISBN-13: 9783540138860

ISBN-10: 3540390960

ISBN-13: 9783540390961

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

Sample text

Tous l e s d d n o m i n a t e u r s s o n t 4 q u i v a - p o u r un d o m a i n e s t r i c t e m e n t p s e u d o - c o n v e x e , o b t e n u e s ne s o n t p a s m e i l l e u r e s que (2). type p o i n t s de m = k < 1-1/2m 0 pap c o n v o l u t i o n , d c r i l . e d e s D~~ = { - ~ < p < - ~ } et passer h la l i m i t e . + + D le passage 5 la limite d4crit plus haut 4tant standard. Posons Sm = Comme -p d' estimer, pour m-1 E k=2 A~m/k( - p)m-2m/k est 4quivalent h assez petit S, + (_p)m-2 .

T H E O R E M E q = i , on 2. - Soient se donne une e cc Q deux boules concentriques dans Ibnction mesurable y > 0 d6finie s u r fin . Si ]0,1] telle que (1) 1 y(r) f0 r dr < +co et v ~ r i f i a n t l ' h y p o t h ~ s e t e c h n i q u e s u i v a n t e (2) ZA > I t e l que sup Y(t) < A . (r) A l o r s il e x i s t e un c o u r a n t T >_ 0 ferm~ de bidegr~ (q,q) sur ~ , dont les 55 masses gT(z,r) s u p ~(z, r) < C ~((r)r 2 n - 2 zEK sup v(z,r) ~ C r 2n-q-1 zEK (4) C = C(K,c)> avec (5) T (6) tout courant ~ et a y a ~ 2£q T sur ~ aucun voisinage ~ de s t r u c t u r e et s u r l ' e x i s t e n c e de d i m e n s i o n : ; sur deux th~or~mes ( D e m a i l l y [21, E1 M i r [4]), ci-dessous r6elle q-1 v~rifie de ® >_ T @ ).

M. Henkin ~ ont obtenu une c a r a c t 6 r i s a t i o n s i m i l a i r e p o u r d e s c l a s s e s h poids de type N e v a n l i n n a . Enfin, A. Bonami et P h . C h a r p e n t i e r ~1~ ont mon- ted q u e c e s c a r a c t d r i s a t i o n s s o n t e n c o r e v r a i e s p o u r c e r t a i n s d o m a i n e s p s e u d o c o n v e x e s de type fini. T o u t e s l e s d d m o n s t r a t i o n s u t i l i s e n t la mgme mdthode, i n s p i r 4 e des t e a v a u x de p L~long F7~ : si x est un s o u s - e n s e m b l e ana~ytique d'un domaine e s t le c o u r a n t d ' i n t d g r a t i o n sue X, tout r e v i e n t ~ r d s o u d r e l ' 6 q u a t i o n a v e c une e s t i m a t i o n c o n v e n a b l e s u r la solution l~6quation idw = 0 , rdsout l'4quation de l ' 4 q u a t i o n b puis, bU = w0, 1' w0,1 a~, u.

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Analyse Complexe: Proceedings of the Journées Fermat - Journées SMF, held at Toulouse, May 24–27, 1983 by E. Bedford, S. Bell (auth.), Eric Amar, Roger Gay, Nguyen Van Thanh (eds.)


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