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Hokkaido University Preprint Series in Mathematics >
Interpolation Of Weighted l^q Sequences By H^p Functions
| 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
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Submitter: 数学紀要登録作業用
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