Banach Journal of Mathematical Analysis

The associated weight and the essential norm of weighted composition operators

Marìa T. Malavé-Ramìrez and Julio C. Ramos-Fernández

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


For an almost radial and typical weight $v$ and any weight $w$, we characterize the continuity, compactness and we estimate the essential norm of weighted composition operators $u C_{\varphi}$, acting from the weighted Banach spaces of analytic functions $H_{v}^{\infty}$ into $H_{w}^{\infty}$, in terms of the quotients of the $w$-norm of the product of $u$ with $\varphi^n$ and the $v$-norm of the $n$th power of the identity function on $\Bbb D$, where $u: \mathbb{D} \to \mathbb{C}$ and $\varphi: \mathbb{D} \to \mathbb{D}$ are analytic. As a consequence, we estimate the essential norm of composition operators $C_\varphi$ (in terms of $\varphi^n$) acting on $\mu$-Bloch spaces, for very general weights $\mu$. We also characterize continuity and compactness of weighted composition operators $uC_\varphi$ acting on $\log$-Bloch space.

Article information

Banach J. Math. Anal., Volume 9, Number 1 (2015), 144-158.

First available in Project Euclid: 19 December 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B33
Secondary: 47B38: Operators on function spaces (general) 30H30: Bloch spaces

Weighted composition operators growth spaces Bloch space


Malavé-Ramìrez, Marìa T.; Ramos-Fernández, Julio C. The associated weight and the essential norm of weighted composition operators. Banach J. Math. Anal. 9 (2015), no. 1, 144--158. doi:10.15352/bjma/09-1-12.

Export citation