Download e-book for iPad: Orderable groups by Mura R.B., Rhemtulla A.

By Mura R.B., Rhemtulla A.

ISBN-10: 0824765796

ISBN-13: 9780824765798

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Example text

J eL 10 c i - 40 Remarque: Le r@sultat num@riques) ment subsiste ~a(L Log+L)(~) et A. Zygmund, (convenablement dans ses parties modifi@ quant aux maJorations essentielles si on suppose (ce r@sultat ne peut @tre am@lior@, Studia Mathematica 26, 1966, iOi-ili). ~ lip ~< Ap E~l ~1 zog+l ~l~x' + A] II r lip. Avant de passer ~ la demonstratzon quelques r@sultats pr@liminaires du th~or~me annonce, etablzssons les suivants. V. 2 - Lemmes pr@paratoires Lemme 9: La convol6e de deux fonctions est - paire si fl et f2 fl et f2' paires ou impaires, ont la m@me parit@ - impaire dans le cas contraire.

Par une est domlnee I s de ~ n. croissantes, r@cl- : @(O) : O. Alors <_ u (u) + v¢(v). 0 Prenant maintenant Vu,v h O, ~(u) = Log(l+u)---~¢(v) uv £ u Log(l+u) = e v - 1, on obtient + v(eV-1) £ u Log(l+u) + ve v. Remarqueimportante: Dans la d@monstration ~ du lemme 8 on a utilis@ uniquement 12(y')ILoglco--~-~Idy'__ < ~. Pour cela il suffit qu'il existe tel que flELP(~). ~ Or pour d'Young avec est un nombre strictement u = 12(y')l, v = xLoglco--~I positif dont on se r@serve 1 i I~(Y')IL°glco--~-~I !

O'NEIL & WEISS "The Hilbert Transform and rearrangement Studia Math,, 5. - CALDERON & ZYGMUND of functions", 2, 1963 "On the existence Acta Math. 85-139. 289-309 integrals", Amer. J. Math.

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Orderable groups by Mura R.B., Rhemtulla A.


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