HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

Nonnegative functions in weighted hardy spaces

Files in This Item:
pre653.pdf65.46 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83806

Title: Nonnegative functions in weighted hardy spaces
Authors: Inoue, Jyunji Browse this author
Nakazi, Takahiko Browse this author
Issue Date: 2004
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

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University