An Analytic Weighted Lipschitz Algebraic Sequence with Closed Ideals



In a series of weighted Lipschitz algebras (4) of a series of analytic functions on the unit disk, we obtain a comprehensive description of closed ideals that satisfies the following requirement
If,(z) - f,(z+8)|
w(181)
o(1) (as 80).
where @ is a continuous modulus meeting certain regularity requirements. The closed ideals of the algebras (Ar) where X1-(2-8):= (log(2-1)+1)+- > 1, in particular, are standard and this resolves Shirokov's query. Namely the weighted Lipschitz algebra possesses a factorization property, ie a sequence of analytic functions and an inner functions such that their quotients belong to the essential algebra of a disk of analytic functions, [Closed ideals of algebras by N.A. Shirokov of B