Carleson measures for analytic Besov spaces
نویسندگان
چکیده
منابع مشابه
Carleson Measures for Analytic Besov Spaces: the Upper Triangle Case
For a large family of weights ρ in the unit disc and for fixed 1 < q < p < ∞, we give a characterization of those measures μ such that, for all functions f holomorphic in the unit disc, ‖f‖Lq(μ) ≤ C(μ) (∫ D |(1− |z|)f ′(z)|pρ(z) m(dz) (1− |z|)2 + |f(0)| ) 1 p .
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In this note we return on the characterization of the Carleson measures for the class of weighted analytic Besov spaces Bp(ρ) considered in [ARS1], Theorem 1. Since our first paper on this topic, we have found shorter or better proofs for some of the intermediate results, which were used in proving various extensions and generalizations of the characterization theorem, [A][ARS2][ARS3]. Here we ...
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Carleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are defined using imbeddings into Lebesgue classes via radial derivatives. The measures, some of which are infinite, are characterized in terms of Berezin transforms and Bergman-metric balls, extending results for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view wit...
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on the associated Bergman tree Tn. Combined with recent results about interpolating sequences this leads, for this range of σ, to a characterization of universal interpolating sequences for B 2 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 H n = B 1/2 2 . We show that μ is a Carleson mea...
متن کاملCarleson Measures on Dirichlet-type Spaces
We show that a maximal inequality holds for the non-tangential maximal operator on Dirichlet spaces with harmonic weights on the open unit disc. We then investigate two notions of Carleson measures on these spaces and use the maximal inequality to give characterizations of the Carleson measures in terms of an associated capacity.
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2002
ISSN: 0213-2230
DOI: 10.4171/rmi/326