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We show that the space of all bounded derivations from the disc algebra intoits dual can be identified with the Hardy space $H^1$; using this, we inferthat all such derivations are compact. Also, given a fixed derivation $D$, weconstruct a finite, positive Borel measure $\mu_D$ on the closed disc, suchthat $D$ factors through $L^2(\mu_D)$. Such a measure is known to exist, forany bounded linear map from the disc algebra to its dual, by results ofBourgain and Pietsch, but these results are highly non-constructive.

Characterising derivations from the disc algebra to its dual