Estimates of essential norms of weighted composition operators between Bloch-type spaces

Olli Hyvärinen; Mikael Lindström

doi:10.1016/j.jmaa.2012.03.059

Estimates of essential norms of weighted composition operators between Bloch-type spaces

Olli Hyvärinen, Mikael Lindström^*

^*Tämän työn vastaava kirjoittaja

Matematiikka

Tutkimustuotos: Lehtiartikkeli › Artikkeli › Tieteellinen › vertaisarvioitu

73 Sitaatiot (Scopus)

Abstrakti

We estimate the essential norm of weighted composition operators uC _φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.

Alkuperäiskieli	Englanti
Sivut	38-44
Sivumäärä	7
Julkaisu	Journal of Mathematical Analysis and Applications
Vuosikerta	393
Numero	1
DOI - pysyväislinkit	https://doi.org/10.1016/j.jmaa.2012.03.059
Tila	Julkaistu - 1 syysk. 2012
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

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10.1016/j.jmaa.2012.03.059

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abstract = "We estimate the essential norm of weighted composition operators uC φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.",

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author = "Olli Hyv{\"a}rinen and Mikael Lindstr{\"o}m",

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AU - Lindström, Mikael

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N2 - We estimate the essential norm of weighted composition operators uC φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.

AB - We estimate the essential norm of weighted composition operators uC φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.

KW - Essential norm

KW - Bloch-type spaces

KW - Weighted composition operator

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U2 - 10.1016/j.jmaa.2012.03.059

DO - 10.1016/j.jmaa.2012.03.059

M3 - Article

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VL - 393

SP - 38

EP - 44

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Estimates of essential norms of weighted composition operators between Bloch-type spaces

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