Carleson measure for analytic Morrey spaces. (September 2015) - Liu, Junming; Lou, Zengjian
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.