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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 6, Pages 3–28 (Mi izv2758)  

This article is cited in 14 scientific papers (total in 14 papers)

Embeddings of model subspaces of the Hardy space: compactness and Schatten–von Neumann ideals

A. D. Baranov

Saint-Petersburg State University

Abstract: We study properties of the embedding operators of model subspaces $K^p_{\Theta}$ (defined by inner functions) in the Hardy space $H^p$ (coinvariant subspaces of the shift operator). We find a criterion for the embedding of $K^p_{\Theta}$ in $L^p(\mu)$ to be compact similar to the Volberg–Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in $K^p_{\Theta}$. We investigate measures $\mu$ such that the embedding operator belongs to some Schatten–von Neumann ideal.

Keywords: Hardy space, inner function, embedding theorem, Carleson measure.


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English version:
Izvestiya: Mathematics, 2009, 73:6, 1077–1100

Bibliographic databases:

UDC: 517.53
MSC: 30D55, 47A45, 47B37
Received: 10.01.2008

Citation: A. D. Baranov, “Embeddings of model subspaces of the Hardy space: compactness and Schatten–von Neumann ideals”, Izv. RAN. Ser. Mat., 73:6 (2009), 3–28; Izv. Math., 73:6 (2009), 1077–1100

Citation in format AMSBIB
\by A.~D.~Baranov
\paper Embeddings of model subspaces of the Hardy space: compactness
and Schatten--von~Neumann ideals
\jour Izv. RAN. Ser. Mat.
\yr 2009
\vol 73
\issue 6
\pages 3--28
\jour Izv. Math.
\yr 2009
\vol 73
\issue 6
\pages 1077--1100

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    This publication is cited in the following articles:
    1. Baranov A., Fricain E., Mashreghi J., “Weighted norm inequalities for de Branges-Rovnyak spaces and their applications”, Amer. J. Math., 132:1 (2010), 125–155  crossref  mathscinet  zmath  isi  elib
    2. G. G. Amosov, A. D. Baranov, V. V. Kapustin, “On perturbations of the isometric semigroup of shifts on the semiaxis”, St. Petersburg Math. J., 22:4 (2011), 515–528  mathnet  crossref  mathscinet  zmath  isi
    3. Baranov A., Dyakonov K., “The Feichtinger conjecture for reproducing kernels in model subspaces”, J. Geom. Anal., 21:2 (2011), 276–287  crossref  mathscinet  zmath  isi  elib
    4. St. Petersburg Math. J., 23:2 (2012), 309–319  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Baranov A., Bessonov R., Kapustin V., “Symbols of truncated Toeplitz operators”, J. Funct. Anal., 261:12 (2011), 3437–3456  crossref  mathscinet  zmath  isi  elib
    6. Zarouf R., “Effective H-Infinity Interpolation Constrained by Weighted Hardy and Bergman Norms”, Ann. Funct. Anal., 2:2 (2011), 59–74  crossref  mathscinet  zmath  isi
    7. G. G. Amosov, A. D. Baranov, V. V. Kapustin, “O primenenii modelnykh prostranstv dlya postroeniya kotsiklicheskikh vozmuschenii polugruppy sdvigov na polupryamoi”, Ufimsk. matem. zhurn., 4:1 (2012), 17–28  mathnet  mathscinet  elib
    8. T. Mengestie, “Schatten class weighted composition operators on weighted Fock spaces”, Arch. Math., 101:4 (2013), 349–360  crossref  mathscinet  zmath  isi
    9. Blandigneres A., Fricain E., Gaunard F., Hartmann A., Ross W., “Reverse Carleson Embeddings for Model Spaces”, J. Lond. Math. Soc.-Second Ser., 88:2 (2013), 437–464  crossref  mathscinet  zmath  isi
    10. Baranov A., Zarouf R., “A Bernstein-Type Inequality for Rational Functions in Weighted Bergman Spaces”, Bull. Sci. Math., 137:4 (2013), 541–556  crossref  mathscinet  zmath  isi  elib
    11. Zarouf R., “Effective H-Infinity Interpolation”, Houst. J. Math., 39:2 (2013), 487–514  mathscinet  zmath  isi  elib
    12. Mengestie T., “Carleson Type Measures For Fock-Sobolev Spaces”, Complex Anal. Oper. Theory, 8:6 (2014), 1225–1256  crossref  mathscinet  zmath  isi
    13. Aleman A., Lyubarskii Yu., Malinnikova E., Perfekt K.-M., “Trace Ideal Criteria For Embeddings and Composition Operators on Model Spaces”, J. Funct. Anal., 270:3 (2016), 861–883  crossref  mathscinet  zmath  isi
    14. Chalendar I., Fricain E., Timotin D., “A Survey of Some Recent Results on Truncated Toeplitz Operators”, Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions, Contemporary Mathematics, 679, eds. Beneteau C., Condori A., Liaw C., Ross W., Sola A., Amer Mathematical Soc, 2016, 59–77  crossref  mathscinet  zmath  isi
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