Difference of composition operators between different Hardy spaces

Shi, Yecheng; Li, Songxiao

doi:10.1016/j.jmaa.2018.04.018

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…The second main result of this study concerns the case when p ă q and ω P p D. It completes in part the main result in [10] which concerns the class D only. An analogue of this result was proved for the Hardy spaces in [27]. Therefore Theorem 3 takes care of the gap consisting of small Bergman spaces that exists between the Hardy and the standard weighted Bergman spaces.…”

Section: Introduction and Main Resultsmentioning

confidence: 90%

Compact differences of composition operators on Bergman spaces induced by doubling weights

Liu¹,

Rättyä²,

Wu³

2020

Preprint

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Bounded and compact differences of two composition operators acting from the weighted Bergman space A p ω to the Lebesgue space L q ν , where 0 ă q ă p ă 8 and ω belongs to the class D of radial weights satisfying a two-sided doubling condition, are characterized. On the way to the proofs a new description of q-Carleson measures for A p ω , with p ą q and ω P D, involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space A p α with ´1 ă α ă 8 to the setting of doubling weights. The case ω P p D is also briefly discussed and an open problem concerning this case is posed.

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Section: Introduction and Main Resultsmentioning

confidence: 90%

Compact differences of composition operators on Bergman spaces induced by doubling weights

Liu¹,

Rättyä²,

Wu³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The second main result of this study concerns the case when p < q and ω ∈ D. It completes in part the main result in [9] which concerns the class D only. An analogue of this result was proved for the Hardy spaces in [26]. Therefore, Theorem 3 takes care of the gap consisting of small Bergman spaces that exists between the Hardy and the standard weighted Bergman spaces.…”

Section: Moreover I Qmentioning

confidence: 90%

Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

Liu

Rättyä

2021

J Geom Anal

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Bounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

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“…authors on several function spaces. See [7,9,10,12,[24][25][26] for example. In 2004, Nieminen and Saksman [16] showed that the compactness of C ϕ − C ψ on H p , with 1 ≤ p < ∞, is independent of p. Very recently, in [2], Choe et al completely characterized compact operators C ϕ − C ψ on H p by using Carleson measures of Bergman spaces.…”

Section: Introductionmentioning

confidence: 99%

Difference of composition-differentiation operators from Hardy spaces to weighted Bergman spaces via harmonic analysis

Shi¹,

Li²

2022

Preprint

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Difference of composition operators between different Hardy spaces

Cited by 8 publications

References 18 publications

Compact differences of composition operators on Bergman spaces induced by doubling weights

Compact differences of composition operators on Bergman spaces induced by doubling weights

Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

Difference of composition-differentiation operators from Hardy spaces to weighted Bergman spaces via harmonic analysis

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