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TESTING SCHATTEN CLASS HANKEL OPERATORS AND CARLESON EMBEDDINGS VIA REPRODUCING KERNELS

Published online by Cambridge University Press:  04 February 2005

M. P. SMITH
M. P. SMITH
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdommps6@york.ac.uk
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Abstract

Criteria are found which classify Schatten class membership for operators on the Hardy space in terms of their action on the reproducing kernels and their derivatives. The Hilbert–Schmidt conditions are shown to be both necessary and sufficient for arbitrary operators. For other Schatten classes, the criteria are shown to be either necessary or sufficient for arbitrary operators, depending upon the exponent of the class. However, using known results of Peller and Luecking, the criteria are shown to be both necessary and sufficient for Hankel operators and Carleson embeddings.

Keywords

47B32 (primary)47B1047B35 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 172 - 186
Copyright
The London Mathematical Society 2005

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