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Riesz's functions and Carleson inequalities

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83597

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
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

Submitter: 数学紀要登録作業用

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