Abstract Analytic Function Theory And Hardy Algebras by K. Barbey, H. König

By K. Barbey, H. König

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Extra info for Abstract Analytic Function Theory And Hardy Algebras

Example text

1O. Choose PP I Qq PQ ~ t p - - + - - - p tq q Thus SPQda = ab iff Assume such that that t>O w i t h LEMMA: DP(o)>O. Then We can u , v ~ 0 we h a v e assume that t P a p = t-qb q. T h e n SPQd~ we QED. Let o£Pos(X,Z) exist a:=~PIILp(o ) and integrate ap I bq ~ tp -- + - ab.

2 < (I + t ( f l o g [ ~1. ( l o g 1=2 MEAN f)l =< I + t ( l o g VALUE Assume a point follows. that -~ .

Measures f Inf~exp(flog L Now f:x~f(x) and d e f i n e can a p p l y that ~(u)=1, = Dp(o) g Put with DP(o) assume is DP(a) f luTPFd~ Inf < which of in q u e s t i o n IlulP(F+e)do < = =< < flog(F+e)dm£ Dp(~) = existence Inf that DP((F+e)~) Inf < f l o g F)+dmE on the m~ Thus gf=1 measures sense, F dm) modulo m6M(~) FJ and hence and hence with m<O. the in any Now in case proved the last larger in ii) QED. the inequality sense, assertion case, Inf DP(o)=O iii) : all remains set of the m6M(~) in the e x t e n d e d fulfilled vial that f r o m the F dm) with From i) the Inf is p r o v e d in i) DP(F~)>O.

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