A norm on the holomorphic Besov space

Bøe, Bjarte

doi:10.1090/s0002-9939-02-06529-2

Cited by 21 publications

(11 citation statements)

References 12 publications

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“…See [4] for more results on inner and outer functions. Using a technique in [2], we give the proof of Theorem 1.1 as follows.…”

Section: Lemma 22 Let (11) and (12) Hold Formentioning

confidence: 99%

On absolute values of QK functions

Bao,

Lou,

Qian

et al. 2016

Preprint

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In this paper, the effect of absolute values on the behavior of functions f in the spaces, but the converse is not always true. For f in the Hardy space H 2 , we give a condition involving the modulus of the function only, such that this condition together with |f | ∈ Q K (∂D) is equivalent to f ∈ Q K . As an application, a new criterion for inner-outer factorisation of Q K spaces is given. These results are also new for Q p spaces.

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“…See [4] for more results on inner and outer functions. Using a technique in [2], we give the proof of Theorem 1.1 as follows.…”

Section: Lemma 22 Let (11) and (12) Hold Formentioning

confidence: 99%

On absolute values of QK functions

Bao,

Lou,

Qian

et al. 2016

Preprint

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“…The characterization of Böe. In [24], Böe obtained an interesting characterization of the norm in analytic Besov spaces in terms of the mean oscillation of the function's modulus with respect to harmonic measure. We give Böe's result in the Dirichlet case.…”

Section: 22mentioning

confidence: 99%

“…Actually, Bishop proved that interpolating sequences for D are also interpolating for M(D), but not the converse. At the present moment, there are four essentially different proofs that (Sep) and (CM) are necessary and sufficient for D interpolation: [21], [24], [25] and [37]. Interpolating sequences for the Dirichlet space differ in one important aspect from interpolating sequences for the Hardy space.…”

Section: Interpolating Sequencesmentioning

confidence: 99%

The Dirichlet space: A Survey

Arcozzi,

Rochberg,

Sawyer

et al. 2010

Preprint

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In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we focus mainly on certain function theoretic properties of the Dirichlet space and omit covering the interesting connections between this space and operator theory. The results discussed in this survey show what is known about the Dirichlet space and compares it with the related results for the Hardy space.

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“…In particular, if s = 0, this gives the classical Besov space B p . We refer to [5], [9], [10] and [12] for B p (s) spaces and [30], [31] and [32] for B 2 (s) = D s spaces. The space B p (ρ) has been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

Multipliers and closures of Besov-type spaces in the Bloch space

Yang

2021

Filomat

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Let p > 1 and let ? be a non-negative function defined in R+. A function f ? H(D) belongs to the space Bp(?) (see [4]) if ||f||p Bp(?) = |f(0)jp + ?D |(1-|z|2) f?(z)|p ?(1-|z|2)/(1-|z|2)2 dA(z) < ?. In this paper, motivated by the works of B?koll? and Bao and G???s, under some conditions on the weight function ?, we investigate the closures CB(B ? Bp(?)) of the spaces B ? Bp(?) in the Bloch space. Moreover we prove that interpolating Blaschke products in CB(B ? Bp(?)) are multipliers of Bp(?) ? BMOA.

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A norm on the holomorphic Besov space

Abstract: Abstract. We obtain a description of the holomorphic Besov space that is valid for the indices 1 ≤ p, q < ∞, 0 < s < 1. Applications to inner-outer factorisation, and to inner functions in particular, are provided.

Cited by 21 publications

References 12 publications

On absolute values of QK functions

On absolute values of QK functions

The Dirichlet space: A Survey

Multipliers and closures of Besov-type spaces in the Bloch space

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