On the maximal ideal space of extended analytic Lipschitz algebras

Let X be a compact, plane set and let K be a compact subset of X. We introduce new classes of Lipschitz algebras Lip(X, K, &#945), lip(X, K, &#945), consisting of those continuous functions f on X such that f|K &#949 Lip(K, &#945), lip(K, &#945), and their analytic subalgebras LipA(X, K, &#945) = Lip(X, K, &#945) &#8745 A(X, K) and lipA(X, K, &#945) = lip(X, K, &#945) &#8745; A(X, K), where 0 < &#945 &#8804; 1 and A(X, K) is the algebra of all continuous complex-valued functions on X, which are analytic on the interior of K. We show that the maximal ideal spaces of these extended Lipschitz algebras coincide with X.Quaestiones Mathematicae 30(2007), 349–35