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We study weighted norm inequalities for the derivatives (Bernstein-type inequalities) in the shift-coinvariant subspaces KΘ p of the Hardy class Hp in the upper half-plane. It is shown that the differentiation operator acts from KΘp to certain spaces of the form Lp (w), where the weight w (x) depends on the density of the spectrum of Θ near the point x of the real line. We discuss an application of the Bernstein-type inequalities to the problems of the description of measures μ, for which KΘp ⊂ Lp (μ), and of compactness of such embeddings. New versions of Carleson-type embedding theorems are obtained generalizing the theorems due to W.S. Cohn and A.L. Volberg-S.R. Treil.
Original language | English |
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Pages (from-to) | 116-146 |
Number of pages | 31 |
Journal | Journal of Functional Analysis |
Volume | 223 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jun 2005 |
ID: 32721757