Closed ideals in analytic weighted Lipschitz algebras

We obtain a complete description of closed ideals in weighted Lipschitz algebras $\Lambda_\omega$ of analytic functions on the unit disk satisfying the following condition $$\frac{|f(z)-f(w)|}{\omega(|z-w|)}=o(1)\qquad(as |z-w| \longrightarrow 0),$$ where $\omega$ is a modulus of continuity satisfying some regularity conditions.