Essential norms and weak compactness of integration operators

Let g be an analytic function on the unit disc and consider the integration operator of the form . We derive estimates for the essential and weak essential norms of T g on the spaces H p and BMOA . In particular, on H 1 and BMOA the operator T g is weakly compact if and only if it is compact.

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Bibliographic Details
Published in:Archiv der Mathematik 2011-07, Vol.97 (1), p.39-48
Main Authors: Laitila, Jussi, Miihkinen, Santeri, Nieminen, Pekka J.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let g be an analytic function on the unit disc and consider the integration operator of the form . We derive estimates for the essential and weak essential norms of T g on the spaces H p and BMOA . In particular, on H 1 and BMOA the operator T g is weakly compact if and only if it is compact.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-011-0272-z