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20 April 2024

» arxiv » 1409.3281

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Essential norm estimates for weighted composition operator on the logarithmic Bloch space
María T. Malavé-RamiÍrez ; Julio C. Ramos-Fernández ;
Date:	11 Sep 2014
Abstract:	In this article, we estimate the essential norm of weighted composition operator $W_{u, varphi}$, acting on the logarithmic Bloch space $mathcal{B}^{v_{log}}$, in terms of the $n$-power of the analytic function $varphi$ and the norm of the $n$-power of the identity function. Also, we estimate the essential norm of the weighted composition operator from $mathcal{B}^{v_{log}}$ into the growth space $H_{v_{log}}^{infty}$. As a consequence of our result, we estimate the essential norm of the composition operator $C_varphi$ acting on the Logarithmic-Zygmund space.
Source:	arXiv, 1409.3281
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