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Weighted estimates are obtained for the derivatives in the model (shiftcoinvariant) subspaces (formula presented), generated by meromorphic inner functions ⊝ of the Hardy class Hp(ℂ+). It is shown that the differentiation operator acts from (formula presented) to a space Lp(w), where the weight w depends on the function ⊝', the rate of growth of the argument of ⊝ along the real line. As an application of the weighted Bernstein-type inequalities, new Carleson-type theorems on embeddings of the subspaces (formula presented) in Lp(μ) are proved. Also, results on the compactness of such embeddings are obtained, and properties of measures μ for which the norms · Lp(μ) and · p are equivalent on a given model subspace (formula presented), are established.
Original language | English |
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Pages (from-to) | 733-752 |
Number of pages | 20 |
Journal | St. Petersburg Mathematical Journal |
Volume | 15 |
Issue number | 5 |
DOIs | |
State | Published - 1 Jan 2004 |
ID: 53517001