2024-03-28T12:26:14Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693662022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Interpolation Of Weighted l^q Sequences By H^p FunctionsNakazi, Takahikoopen accessweighted Hardy spaceweighted sequence spaceinterpolation410Let (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.Department of Mathematics, Hokkaido University2003-11-29engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83762http://hdl.handle.net/2115/6936610.14943/83762Hokkaido University Preprint Series in Mathematics617111https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69366/1/pre617.pdfapplication/pdf120.16 KB2003-11-29