Carleson measure for analytic Morrey spaces. (September 2015)

• Record Type: Journal Article
• Authors: Liu, Junming; Lou, Zengjian
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 423
• Page End: 432
• Publication Date: 2015-09
• Subjects: 28A -- 30H -- 47B; Analytic Morrey spaces -- Carleson measure -- Boundedness -- Compactness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let μ be a positive Borel measure on the unit disc D . In this note, we show that the inclusion mapping from analytic Morrey spaces L 2, λ ( D ) to quadratic tent-type spaces T λ ∞ ( μ ) is bounded (compact) if and only if μ is a Carleson measure (vanishing Carleson measure). As a byproduct we get a new version of well-known Carleson measure theorem of Hardy spaces. The inverse Carleson measure problem of L 2, λ ( D ) is also studied.