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Nonnegative functions in weighted hardy spaces
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

Submitter: 数学紀要登録作業用
