The classical Dirichlet space is a complete Pick space, hence by a theorem of Agler and McCarthy, there exists an embedding b of the unit disc into a d-dimensional ball such that composition with b realizes the Dirichlet space as a quotient of the Drury-Arveson space. We show that d =∞ is necessary, even if we only demand that composition with b induces a surjective map between the multiplier algebras.

The author was partially supported by a GIF grant.