Multipliers for the Calderón Construction

Abstract

On the basis of a new approach to the Calderón construction \(X_0^{\theta} X_1^{1-\theta}\) for ideal spaces \(X_0\) and \(X_1\) and a parameter \(\theta \in [0,1]\), final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces \(X_0\) and \(X_1\) have the Fatou property, then \(M(X_0^{\theta_0} X_1^{1-\theta_0}\,{\to}\,X_0^{\theta_1} X_1^{1-\theta_1}) = M(X_1^{\theta_1 - \theta_0} \to X_0^{\theta_1 -\theta_0})\) for \(0 <\theta_0 <\theta_1 <1\). Due to the absence of constraints on the ideal spaces \(X_0\) and \(X_1\), the obtained results apply to a large class of ideal spaces.