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Published online by Cambridge University Press: 20 November 2018
We obtain a complete description of closed ideals of the algebra $\mathcal{D}\cap \text{li}{{\text{p}}_{\alpha }},0<\alpha \le \frac{1}{2}$, where
$\mathcal{D}$ is the Dirichlet space and
$\text{li}{{\text{p}}_{\alpha }}$ is the algebra of analytic functions satisfying the Lipschitz condition of order
$\alpha $.