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Riesz's functions and Carleson inequalities
| Title: | Riesz's functions and Carleson inequalities |
| Authors: | Nakazi, T. Browse this author |
| Keywords: | Bergman space | | weight | | Riesz's function | | Carleson inequality | | interpolation sequence |
| Issue Date: | 1-Feb-1999 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 451 |
| Start Page: | 1 |
| End Page: | 9 |
| Abstract: | Let µ be a finite positive Borel measure on the open unit disc D and H a set of all analytic functions on D. For each a in D, put r(µ, a)= sup lf(a)J2 where .f EH and klfl2dµ ::; 1. Unless the support set ofµ is a finite set, fnr(µ, a)dµ(a) ∞. However zED sup }f Dt(z) r(µ, a)dµ(a) < ∞ may happen where Dt(z) denotes the Bergman disc in D. We study when this is possible. When vis a descrete measure such that dv = I:s(µ,a)8a,zED sup/, D1(z) r(µ, a)dv(a) Under some condition onµ, we show that zsup eDJf D1(z) r(µ,a)dv(a) < ∞ for a finite positive Borel measure v on D if and only if ( v, µ )-Carleson inequality is valid. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69201 |
| 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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