Hokkaido University | Library | HUSCAP Advanced Search 言語 日本語 English

Nonnegative functions in weighted hardy spaces

Files in This Item:
 pre653.pdf 65.46 kB PDF View/Open
 Title: Nonnegative functions in weighted hardy spaces Authors: Inoue, Jyunji Browse this author Nakazi, Takahiko Browse this author Issue Date: 2004 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 653 Start Page: 1 End Page: 9 Abstract: Let $W$ be a nonnegative summable function whose logarithm is also summable with respect to the Lebesgue measure on the unit circle. For $0 < p < \infty,_*_H^p(W)$ denotes a weighted Hardy space on the unit circle. When $W \equiv 1,_*_H^p(W)$ is the usual Hardy space $H^p$. We are interested in $H^p(W)_+$ the set of all nonnegative functions in $H^p(W)$. If $p \geq 1/2,_*_H^p_+$ consists of constant functions. However $H^p(W)_+$ contains a nonconstant nonnegative function for some weight $W$. In this paper, if $p \geq 1/2$ we determine $W$ and describe $H^p(W)_+$ when the linear span of $H^p(W)_+$ is of finite dimension. Moreover we show that the linear span of $H^p(W)_+$ is of infinite dimension for arbitrary weight $W$ when $0 < p < 1/2$. Type: bulletin (article) URI: http://hdl.handle.net/2115/69460 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics