Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496007 | Journal of Functional Analysis | 2005 | 31 Pages |
Abstract
We study weighted norm inequalities for the derivatives (Bernstein-type inequalities) in the shift-coinvariant subspaces KÎp of the Hardy class Hp in the upper half-plane. It is shown that the differentiation operator acts from KÎp to certain spaces of the form Lp(w), where the weight w(x) depends on the density of the spectrum of Î 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 KÎpâLp(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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
A.D. Baranov,