Multipliers and integration operators between conformally invariant spaces

Girela, Daniel; Merchán, Noel

doi:10.1007/s13398-020-00918-z

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Isometric Multiplication Operators2

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2020

2024

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Cited by 5 publications

(2 citation statements)

References 42 publications

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“…Hence, if M u is an isometry of BMOA then u must be an H ∞ function with H ∞ -norm smaller than or equal to 1. This can be seen in [18][19][20].…”

Section: Isometric Multiplication Operatorsmentioning

confidence: 85%

Isometric multiplication operators and weighted composition operators of BMOA

Geng

2021

J Inequal Appl

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Let u be an analytic function in the unit disk $\mathbb{D}$ D and φ be an analytic self-map of $\mathbb{D}$ D . We give characterizations of the symbols u and φ for which the multiplication operator $M_{u}$ M u and the weighted composition operator $M_{u,\varphi }$ M u , φ are isometries of BMOA.

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“…Hence, if M u is an isometry of BMOA then u must be an H ∞ function with H ∞ -norm smaller than or equal to 1. This can be seen in [18][19][20].…”

Section: Isometric Multiplication Operatorsmentioning

confidence: 85%

Isometric multiplication operators and weighted composition operators of BMOA

Geng

2021

J Inequal Appl

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“…The spaces of multipliers M(B p , B q ) have been studied in a good number of papers (see [4,12,15,16,27,28,31] and the references therein). In particular, the following result holds.…”

Section: An Application Of Theorem 11 To Multipliersmentioning

confidence: 99%

Radial growth of the derivatives of analytic functions in Besov spaces

Domínguez

Girela

2020

Concrete Operators

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For 1 < p < ∞, the Besov space Bp consists of those functions f which are analytic in the unit disc 𝔻 = {z ∈ 𝔺 : |z| < 1} and satisfy ∫𝔻(1 − |z|2)p−2|f ′(z)|p dA(z) < ∞. The space B2 reduces to the classical Dirichlet space 𝒟. It is known that if f ∈ 𝒟then |f ′(reiθ)| = o[(1 − r)−1/2], for almost every ∈ [0, 2π]. Hallenbeck and Samotij proved that this result is sharp in a very strong sense. We obtain substitutes of the above results valid for the spaces Bp (1 < p < ∞) an we give also an application of our them to questions concerning multipliers between Besov spaces.

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Some properties of the integration operators on the spaces F(p, q, s)

Chen

2023

Acta Math Sci

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Multipliers and integration operators between conformally invariant spaces

Cited by 5 publications

References 42 publications

Isometric multiplication operators and weighted composition operators of BMOA

Isometric multiplication operators and weighted composition operators of BMOA

Radial growth of the derivatives of analytic functions in Besov spaces

Some properties of the integration operators on the spaces F(p, q, s)

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