# Bilinear forms on the Dirichlet space

@article{Arcozzi2008BilinearFO, title={Bilinear forms on the Dirichlet space}, author={Nicola Arcozzi and Richard Rochberg and Eric Sawyer and Brett D. Wick}, journal={Analysis \& PDE}, year={2008}, volume={3}, pages={21-47} }

Let $\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by $T_{b}(f,g):= _{\mathcal{D}} $, where we are looking at the inner product in the space $\mathcal{D}$.
We let the norm of $T_{b}$ denotes its norm as a bilinear map from $\mathcal{D}\times\mathcal{D}$ to the complex numbers. We say a function $b$ is in the… Expand

#### 32 Citations

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Bilinear forms on potential spaces in the unit circle

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Abstract In this paper we characterize the boundedness on the product of Sobolev spaces Hs(𝕋) × Hs(𝕋) on the unit circle 𝕋, of the bilinear form Λb with symbol b ∈ Hs(𝕋) given by $${{\Lambda}_b}… Expand

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Let μ[mu] be a nonnegative Borel measure on the boundary T[unit circle] of the unit disc and define φμ[phi mu] to be the harmonic function φμ(z) = ∫ [integral]T 1− |z|[square] |ζ[zeta]− z|2 dμ(ζ).… Expand

Hankel Forms and Embedding Theorems in Weighted Dirichlet Spaces

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We show that for a fixed operator-valued analytic function $g$ the boundedness of the bilinear (Hankel-type) form
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On the Dirichlet space D, we show that there is a multiplier f of D such that $$M_f$$Mf is not essentially hyponormal, i.e. $$\pi (M_f)$$π(Mf) is not hyponormal in the Calkin algebra $$B(D)/\mathcal… Expand

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