Bernstein-type inequalities for shift-coinvariant subspaces and their applications to Carleson embeddings

By A. Baranov. 2005

53 citations recorded by the source corpus.

Abstract We study weighted norm inequalities for the derivatives (Bernstein-type inequalities) in the shift-coinvariant subspaces K Θ p of the Hardy class H p in the upper half-plane. It is shown that the differentiation operator acts from K Θ p to certain spaces of the form L p ( 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 K Θ p ⊂ L p ( 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5174a0eb6882c4ecd8627c53c607c1ac29fa8d88

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In Applied Mathematics

1. Y. Belov
2. T. Mengestie
3. Kristian Seip
4. A. Baranov
5. Roman V. Bessonov
6. V. Kapustin
7. Chun-Kit Lai

In Mathematical Physics

1. Y. Belov
2. T. Mengestie
3. Kristian Seip
4. A. Baranov

Citations in the corpus

• Symbols of truncated Toeplitz operators (2010, background): “Many partial results may be found in [18, 19, 33, 6, 26, 7, 8].”
• Discrete Hilbert transforms on sparse sequences (2009, background): “Other partial results can be found in [2, 3, 4, 17, 19, 31].”