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Bilinear forms on vector Hardy spaces

Published online by Cambridge University Press:  18 May 2009

Gordon Blower
Gordon Blower
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster Lai 4Yf, England, U.K.
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Abstract

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Let φ: ℋ → be a bilinear form on vector Hardy space. Introduce the symbol φ of Φ by (φ (Z1, Z2), a ⊗ b) = Φ (K21 ⊗ a, K22 ⊗ b ), where Kw is the reproducing kernel for w ∈ D. We show that Φ extends to a bounded bilinear form on provided that the gradient defines a Carleson measure in the bidisc D2. We obtain a sufficient condition for Φ to extend to a Hilbert space. For vectorial bilinear Hankel forms we obtain an analogue of Nehari's Theorem.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 371 - 378
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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