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Carleson Measures on Spaces of Hardy-Sobolev Type

Published online by Cambridge University Press:  20 November 2018

Carme Cascante  and
Joaquín M. Ortega
Carme Cascante
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi Facultat de Matemàtiques Universitat de Barcelona Gran Via585 08071 Barcelona e-mail: cascante@cerber.mat.ub.esortega@cerber.mat.ub.es
Joaquín M. Ortega
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi Facultat de Matemàtiques Universitat de Barcelona Gran Via585 08071 Barcelona e-mail: cascante@cerber.mat.ub.esortega@cerber.mat.ub.es
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Abstract

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We study positive measures on 𝔹n satisfying that . for any ƒ ∈ where is the Hardy-Sobolev space in the unit ball. We obtain several computable sufficient conditions as well as some necessary conditions and establish their sharpness. We study the same problem for Besov-Sobolev spaces and give some applications to multipliers.

Keywords

32A3531C15Carleson measureholomorphic functions in the unit ballnon-isotropic potentialsHardy-Sobolev spacesBesov-Sobolev spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 6 , 01 December 1995 , pp. 1177 - 1200
Copyright
Copyright © Canadian Mathematical Society 1995

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