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^*

^*Corresponding author for this work

Mathematics

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

75 Citations (Scopus)

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.

Original language	English
Pages (from-to)	38-44
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	393
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.03.059
Publication status	Published - 1 Sept 2012
MoE publication type	A1 Journal article-refereed

Keywords

Essential norm
Bloch-type spaces
Weighted composition operator

Access to Document

10.1016/j.jmaa.2012.03.059

Cite this

@article{174ba146f38c410691148c8ef20317bb,

title = "Estimates of essential norms of weighted composition operators between Bloch-type spaces",

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.",

keywords = "Essential norm, Bloch-type spaces, Weighted composition operator",

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

year = "2012",

month = sep,

day = "1",

doi = "10.1016/j.jmaa.2012.03.059",

language = "English",

volume = "393",

pages = "38--44",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Estimates of essential norms of weighted composition operators between Bloch-type spaces

AU - Hyvärinen, Olli

AU - Lindström, Mikael

PY - 2012/9/1

Y1 - 2012/9/1

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

UR - https://www.scopus.com/pages/publications/84860759720

U2 - 10.1016/j.jmaa.2012.03.059

DO - 10.1016/j.jmaa.2012.03.059

M3 - Article

SN - 0022-247X

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this