Multipliers for the Calder\'on construction

E. I. Berezhnoi

Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 3-17

Résumé

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.

Détail

Keywords: ideal Banach space, pointwise multiplier, local Morrey space.
Mots-clés : Calderón construction