Composition operators on Besov and Dirichlet type spaces of the ball

Pons, Matthew A.

doi:10.1007/bf03651309

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…Proof. This result for a special case has been pointed out by Pons [18], without proof. For completeness, we give a simple proof.…”

Section: The Commutator On the Dirichlet Spacementioning

confidence: 51%

“…Theorem C. (Theorem 7 in [18]) Let ϕ be a linear fractional self-map of B N and K w be the reproducing kernel of D(B N ). Then for f ∈ D(B N ), we have…”

Section: Preliminariesmentioning

confidence: 99%

“…s 1 < s < s 2 < ∞, complex interpolation theorem for the weighted Dirichlet space D s (B N ) tells us[D s 1 , D s 2 ] θ = D s with s = (1 − θ)s 1 + θs 2 for θ ∈ (0, 1) (see Proposition 1 of[18]). Choosing s 1 = −n and s 2 = 2, then for linear fractional self-maps ϕ and ψ of B N , the operatorC ϕ − C ψ is bounded on D −n (B N ) and D 2 (B N ) = A 2 (B N ).…”

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confidence: 99%

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Commutators of automorphic composition operators with adjoints

Jiang

2014

Preprint

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In this paper, we investigate the compactness of the commutator [C * ψ , Cϕ] on the Hardy space H 2 (BN ) or the weighted Bergman space A 2 s (BN ) (s > −1), when ϕ and ψ are automorphisms of the unit ball BN . We obtain that [C * ψ , Cϕ] is compact if and only if ϕ and ψ commute and they are both unitary. This generalizes the corresponding result in one variable. Moreover, our technique is different and simpler. In addition, we also discuss the commutator [C * ψ , Cϕ] on the Dirichlet space D(BN ), where ϕ and ψ are linear fractional self-maps or both automorphisms of BN .

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“…Proof. This result for a special case has been pointed out by Pons [18], without proof. For completeness, we give a simple proof.…”

Section: The Commutator On the Dirichlet Spacementioning

confidence: 51%

“…Theorem C. (Theorem 7 in [18]) Let ϕ be a linear fractional self-map of B N and K w be the reproducing kernel of D(B N ). Then for f ∈ D(B N ), we have…”

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

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Commutators of automorphic composition operators with adjoints

Jiang

2014

Preprint

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“…She would like to express her gratitude to them. She is also grateful to Matthew A. Pons for providing the references [15] and [18].…”

Section: Acknowledgementsmentioning

confidence: 99%

Essential normality of automorphic composition operators

Jiang¹,

Ouyang²,

Zhao³

2016

Acta Sci. Math.

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“…Every parabolic disk automorphism is conformally equivalent to one whose fixed point (of multiplicity 2) is 1. [40]). Let ϕ be a parabolic disk automorphism.…”

Section: Spectra Of Composition Operators With Symbols Of Disk Automo...mentioning

confidence: 99%