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

Baranov, Anton

doi:10.1070/im2009v073n06abeh002473

Cited by 20 publications

(28 citation statements)

References 24 publications

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“…We return to the the original ideas of Cohn [6] and extend embedding operators on K ϑ to operators acting on the Hardy-Smirnov space E 2 (D) of a certain domain D ⊃ D. This allows us to obtain a geometrical criterion for the inclusion of I µ in S p . In particular we recover the aforementioned result in [4].…”

Section: Introductionsupporting

confidence: 82%

Trace ideal criteria for embeddings and composition operators on model spaces

Aleman¹,

Lyubarskii²,

Malinnikova³

et al. 2016

Journal of Functional Analysis

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Let K ϑ be a model space generated by an inner function ϑ. We study the Schatten class membership of embeddings I : K ϑ ֒→ L 2 (µ), µ a positive measure, and of composition operators Cϕ :In the case of onecomponent inner functions ϑ we show that the problem can be reduced to the study of natural extensions of I and Cϕ to the Hardy-Smirnov space E 2 (D) in some domain D ⊃ D. In particular, we obtain a characterization of Schatten membership of Cϕ in terms of Nevanlinna counting function. By example this characterization does not hold true for general ϑ.

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Section: Introductionsupporting

confidence: 82%

Trace ideal criteria for embeddings and composition operators on model spaces

Aleman¹,

Lyubarskii²,

Malinnikova³

et al. 2016

Journal of Functional Analysis

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“…What is called therein the second vanishing condition is easier to state. We say that µ satisfies the second (Θ, ǫ)-vanishing condition [7,14] if for each η > 0 there exists δ > 0 such that µ(S(I))/|I| < η whenever |I| < δ and S(I) ∩ Ω(Θ, ǫ) = ∅. The following result is then proved in [7].…”

Section: Embedding Of Model Spacesmentioning

confidence: 98%

“…We say that µ satisfies the first (Θ, ǫ)-vanishing condition if these Carleson constants tend to 0 when δ → 0. It is shown in [7] that the first vanishing condition implies the second, and that the converse is not true: there exist measures which satisfy the second vanishing condition but not the first.…”

Section: Embedding Of Model Spacesmentioning

confidence: 99%

A survey of some recent results on truncated Toeplitz operators

Chalendar¹,

Fricain²,

Timotin³

2016

Recent Progress on Operator Theory And Approximation in Spaces of Analytic Functions

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Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and spectra of these operators to properties of their symbols. We also connect these facts with properties of the natural embedding measures associated to these operators.2010 Mathematics Subject Classification. 30J05, 30H10, 46E22.

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“…Carleson measures were first introduced by L. Carleson [4] as a tool to study interpolating sequences in the Hardy space H ∞ of bounded analytic functions in the unit disc and the corona problem. Since then the measures have found numerous applications and extensions in the study of various spaces of functions: for example see [1,2,3,7,10,11,18,23,27]. In this paper, we study one of its extensions namely the (p, q) Fock-Carleson measures for weighted Fock-Sobolev spaces.…”

Section: The (P Q) Fock-carleson Measures On Fock-sobolev Spacesmentioning

confidence: 99%

Carleson Type Measures for Fock–Sobolev Spaces

Mengestie

2013

Complex Anal. Oper. Theory

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Abstract. We describe the (p, q) Fock-Carleson measures for weighted Fock-Sobolev spaces in terms of the objects (s, t)-Berezin transforms, averaging functions, and averaging sequences on the complex space C n . The main results show that while these objects may have growth not faster than polynomials to induce the (p, q) measures for q ≥ p, they should be of L p/(p−q) integrable against a weight of polynomial growth for q < p. As an application, we characterize the bounded and compact weighted composition operators on the Fock-Sobolev spaces in terms of certain Berezin type integral transforms on C n . We also obtained estimation results for the norms and essential norms of the operators in terms of the integral transforms. The results obtained unify and extend a number of other results in the area.Mathematics Subject Classification (2010). 31B05, 39A12,31C20.

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

Cited by 20 publications

References 24 publications

Trace ideal criteria for embeddings and composition operators on model spaces

Trace ideal criteria for embeddings and composition operators on model spaces

A survey of some recent results on truncated Toeplitz operators

Carleson Type Measures for Fock–Sobolev Spaces

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