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Interpolation Of Weighted l^q Sequences By H^p Functions

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83762

Title: Interpolation Of Weighted l^q Sequences By H^p Functions
Authors: Nakazi, Takahiko Browse this author
Keywords: weighted Hardy space
weighted sequence space
interpolation
Issue Date: 29-Nov-2003
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 617
Start Page: 1
End Page: 11
Abstract: Let (znQ ) be a sequence of points in the open unit disc D and ½n = m6=n j(zn ¡zm)(1¡ ¯zmzn)¡1j > 0. Let a = (aj)1j =1 be a sequence of positive numbers and `s(a) = f(wj) ; (ajwj) 2 `sg where 1 · s · 1. When 1 · p · 1 and 1=p + 1=q = 1, we show that f(f(zn)) ; f 2 Hpg ¾ `s(a) if and only if there exists a finite positive constant ° such that ( 1X n=1 (an½n)¡t(1 ¡ jznj2)tjf(zn)jt )1=t · °kfkq (f 2 Hq), where 1=s+1=t = 1. As results, we show that f(f(zj)) ; f 2 Hpg ¾ `1(a) if and only if sup n (an½n)¡1(1¡jznj2)1=p < 1, and f(f(zn)) ; f 2 H1g ¾ `1(a) if and only if X n (an½n)¡1(1 ¡ jznj2)±zn is finite measure on D. These are also proved in the case of weighted Hardy spaces.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69366
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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