Coefficient multipiers of Lipschitz functions (Q1324906)

The author studies multipliers on Lipschitz spaces of holomorphic functions in the unit disc (a holomorphic function is identified with the sequence of its Taylor coefficients, and multipliers are multiplication operators on this sequence space). The main result states the coincidence of the sets of multipliers from \(L_ \infty\)- and \(L_ 2\)-versions of Lipschitz spaces to a class of target spaces. This allows to describe some multiplier spaces. The results are applied to trigonometric series and are partially generalized to the case of the unit ball in \(\mathbb{C}^ n\).