Volterra type operators between Bloch type spaces and weighted Banach spaces

2018/08/28 by Qingze Lin, Lin, Qingze
Mathematics · #30H05 #47G10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1808.09404

openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When the weight μ is more general than normal, the complete characterizations in terms of the symbol g and weights for the conditions of the boundedness and compactness of T_g: H^∞_ν→ H^∞_μ and S_g: H^∞_ν→ H^∞_μ are still unknown. Smith et al. firstly gave the sufficient and necessary conditions for the boundedness of Volterra type operators on Banach spaces of bounded analytic functions when the symbol functions are univalent. In this paper, continuing their lines of investigations, we give the complete characterizations of the conditions for the boundedness and compactness of Volterra type operators T_g and S_g between Bloch type spaces B^∞_ν and weighted Banach spaces H^∞_ν with more general weights, which generalize their works.

Citations

• The Q p Carleson measure problem

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