Closed ideals in analytic weighted Lipschitz algebras

Abstract

We obtain a complete description of closed ideals in weighted Lipschitz algebras Λ ω of analytic functions on the unit disk satisfying the following condition | f ( z ) − f ( w ) | ω ( | z − w | ) = o ( 1 ) ( as | z − w | → 0 ) , where ω is a modulus of continuity satisfying some regularity conditions. In particular the closed ideals of the algebras Λ χ α , where χ α ( t ) : = 1 ( | log ( t ) | + 1 ) α , α > 0 , are standard and this answers Shirokov's question [N.A. Shirokov, Closed ideals of algebras of B p q α -type, Izv. Akad. Nauk SSSR Mat. 46 (6) (1982) 1316–1333 (in Russian), p. 587].