Carleson measure for analytic Morrey spaces

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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 L2,λ(D) to quadratic tent-type spaces Tλ∞(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 L2,λ(D) is also studied.