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

2014/09/11 by María T. Malavé-RamiÍrez, Malavé-RamiÍrez, María T., Julio C. Ramos-Fernández +1
Mathematics · #30H30 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary 46B33 #Secondary 47B38

paper · pdf · doi:10.48550/arxiv.1409.3281

openalex publication_date 2014/09/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this article, we estimate the essential norm of weighted composition operator W_{u, φ}, acting on the logarithmic Bloch space B^v_log, in terms of the n-power of the analytic function φ and the norm of the n-power of the identity function. Also, we estimate the essential norm of the weighted composition operator from B^v_log into the growth space H_v_log^∞. As a consequence of our result, we estimate the essential norm of the composition operator C_φ acting on the Logarithmic-Zygmund space.

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