Composition operators between weighted banach spaces of analytic functions

J. Bonet; P. Domański; M. Lindström; J. Taskinen

doi:10.1017/s1446788700001336

Composition operators between weighted banach spaces of analytic functions

J. Bonet^*
, P. Domański
, M. Lindström
, J. Taskinen

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

139 Citations (Scopus)

Abstract

We characterize those analytic self-maps φ of the unit disc which generate bounded or compact composition operators C_φ between given weighted Banach spaces H^∞_v or H⁰_v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

Original language	English
Pages (from-to)	101-118
Number of pages	18
Journal	Journal of the Australian Mathematical Society
Volume	64
Issue number	1
DOIs	https://doi.org/10.1017/s1446788700001336
Publication status	Published - Feb 1998
MoE publication type	A1 Journal article-refereed

Funding

The research of the first named author was partially supported by DGICYT, grant, no. PB94 - 0541. The research of the second named author was mainly done while he visited Universidad Politecnica de Valencia, Spain, supported by DGICYT (Spain), grant no. SAB 95-0092 in the academic year 1995/96. © 1998 Australian Mathematical Society 0263-6115/98 $A2.00 + 0.00

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abstract = "We characterize those analytic self-maps φ of the unit disc which generate bounded or compact composition operators Cφ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.",

author = "J. Bonet and P. Doma{\'n}ski and M. Lindstr{\"o}m and J. Taskinen",

note = "Funding Information: The research of the first named author was partially supported by DGICYT, grant, no. PB94 - 0541. The research of the second named author was mainly done while he visited Universidad Politecnica de Valencia, Spain, supported by DGICYT (Spain), grant no. SAB 95-0092 in the academic year 1995/96. {\textcopyright} 1998 Australian Mathematical Society 0263-6115/98 \$A2.00 + 0.00",

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AU - Domański, P.

AU - Lindström, M.

AU - Taskinen, J.

N1 - Funding Information: The research of the first named author was partially supported by DGICYT, grant, no. PB94 - 0541. The research of the second named author was mainly done while he visited Universidad Politecnica de Valencia, Spain, supported by DGICYT (Spain), grant no. SAB 95-0092 in the academic year 1995/96. © 1998 Australian Mathematical Society 0263-6115/98 $A2.00 + 0.00

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N2 - We characterize those analytic self-maps φ of the unit disc which generate bounded or compact composition operators Cφ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

AB - We characterize those analytic self-maps φ of the unit disc which generate bounded or compact composition operators Cφ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

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DO - 10.1017/s1446788700001336

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EP - 118

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

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ER -

Composition operators between weighted banach spaces of analytic functions

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