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arXiv · 1409.3281

Essential norm estimates for weighted composition operator on the logarithmic Bloch space

María T. Malavé-RamiÍrez·Julio C. Ramos-Fernández
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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.

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María T. Malavé-RamiÍrez, Julio C. Ramos-Fernández. 2014-09-11. Essential norm estimates for weighted composition operator on the logarithmic Bloch space. https://arxiv.org/abs/1409.3281

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