Geodesic
Bilinear forms on vector Hardy spaces
Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 371-378

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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. 
Blower, Gordon. Bilinear forms on vector Hardy spaces. Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 371-378. doi: 10.1017/S0017089500032286
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