کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668054 1345494 2008 74 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Carleson measures for the Drury–Arveson Hardy space and other Besov–Sobolev spaces on complex balls
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Carleson measures for the Drury–Arveson Hardy space and other Besov–Sobolev spaces on complex balls
چکیده انگلیسی

For 0⩽σ<1/20⩽σ<1/2 we characterize Carleson measures μ   for the analytic Besov–Sobolev spaces B2σ on the unit ball BnBn in CnCn by the discrete tree condition∑β⩾α[2σd(β)I*μ(β)]2⩽CI*μ(α)<∞,α∈Tn, on the associated Bergman tree TnTn. Combined with recent results about interpolating sequences this leads, for this range of σ  , to a characterization of universal interpolating sequences for B2σ and also for its multiplier algebra.However, the tree condition is not   necessary for a measure to be a Carleson measure for the Drury–Arveson Hardy space Hn2=B21/2. We show that μ   is a Carleson measure for B21/2 if and only if both the simple condition2d(α)I*μ(α)⩽C,α∈Tn, and the split tree condition∑k⩾0∑γ⩾α2d(γ)−k∑(δ,δ′)∈G(k)(γ)I*μ(δ)I*μ(δ′)⩽CI*μ(α),α∈Tn, hold. This gives a sharp estimate for Drury's generalization of von Neumann's operator inequality to the complex ball, and also provides a universal characterization of Carleson measures, up to dimensional constants, for Hilbert spaces with a complete continuous Nevanlinna–Pick kernel function.We give a detailed analysis of the split tree condition for measures supported on embedded two manifolds and we find that in some generic cases the condition simplifies. We also establish a connection between function spaces on embedded two manifolds and Hardy spaces of plane domains.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 218, Issue 4, 10 July 2008, Pages 1107–1180
نویسندگان
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