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Weighted bernstein-type inequalities, and embedding theorems for the model subspaces. / Baranov, A. D.

In: St. Petersburg Mathematical Journal, Vol. 15, No. 5, 01.01.2004, p. 733-752.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranov, AD 2004, 'Weighted bernstein-type inequalities, and embedding theorems for the model subspaces', St. Petersburg Mathematical Journal, vol. 15, no. 5, pp. 733-752. https://doi.org/10.1090/S1061-0022-04-00829-5

APA

Baranov, A. D. (2004). Weighted bernstein-type inequalities, and embedding theorems for the model subspaces. St. Petersburg Mathematical Journal, 15(5), 733-752. https://doi.org/10.1090/S1061-0022-04-00829-5

Vancouver

Baranov AD. Weighted bernstein-type inequalities, and embedding theorems for the model subspaces. St. Petersburg Mathematical Journal. 2004 Jan 1;15(5):733-752. https://doi.org/10.1090/S1061-0022-04-00829-5

Author

Baranov, A. D. / Weighted bernstein-type inequalities, and embedding theorems for the model subspaces. In: St. Petersburg Mathematical Journal. 2004 ; Vol. 15, No. 5. pp. 733-752.

BibTeX

@article{c75790c6bf86437fa2cd1c15351aaa4b,
title = "Weighted bernstein-type inequalities, and embedding theorems for the model subspaces",
abstract = "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.",
keywords = "Bernstein-type inequality, Hardy class, Inner function, Shift-coinvariant subspace",
author = "Baranov, {A. D.}",
year = "2004",
month = jan,
day = "1",
doi = "10.1090/S1061-0022-04-00829-5",
language = "English",
volume = "15",
pages = "733--752",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "5",

}

RIS

TY - JOUR

T1 - Weighted bernstein-type inequalities, and embedding theorems for the model subspaces

AU - Baranov, A. D.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

KW - Bernstein-type inequality

KW - Hardy class

KW - Inner function

KW - Shift-coinvariant subspace

UR - http://www.scopus.com/inward/record.url?scp=85009801626&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-04-00829-5

DO - 10.1090/S1061-0022-04-00829-5

M3 - Article

AN - SCOPUS:85009801626

VL - 15

SP - 733

EP - 752

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 53517001