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

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 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 Publisher: Department of Mathematics, Hokkaido University 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