Some Closed Range Integral Operators on Spaces of Analytic Functions

Our main result is a characterization of g for which the operator is bounded below on the Bloch space. We point out analogous results for the Hardy space H 2 and the Bergman spaces A p for 1 ≤ p < ∞. We also show the companion operator is never bounded below on H 2 , Bloch, nor BMOA , but may be...

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Bibliographic Details
Published inIntegral equations and operator theory Vol. 69; no. 1; pp. 87 - 99
Main Author Anderson, Austin
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.01.2011
Subjects
Analysis
Mathematics
Mathematics and Statistics
BMOA
multiplication operator
Bergman
Hardy
integral operator
30D45
closed range
Secondary 47G10
Volterra operator
Cesaro operator
bounded below
Primary 47B38
Bloch
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ISSN0378-620X
1420-8989
DOI10.1007/s00020-010-1827-2

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Summary:Our main result is a characterization of g for which the operator is bounded below on the Bloch space. We point out analogous results for the Hardy space H 2 and the Bergman spaces A p for 1 ≤ p < ∞. We also show the companion operator is never bounded below on H 2 , Bloch, nor BMOA , but may be bounded below on A p .
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-010-1827-2