Volterra type operators on minimal Mobius invariant space

2021/12/16 by Huayou Xie, Xie, Huayou, Jun‐Ming Liu +3
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2112.08675

openalex publication_date 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we mainly study operator-theoretic properties on Besov space B₁ on the unit disc. This space is the minimal Mobius invariant space. Firstly, we consider the boundedness of Volterra type operators. Secondly, we prove that Volterra type operators belong to the Deddens algebra of composition operator. Thirdly, we obtain estimates for the essential norm of Volterra type operators. Finally, we give a complete characterization of spectrum of Volterra type operators.

Related

• Product-type operators between minimal Möbius invariant spaces and Zygmund type spaces
• Essential norms of Volterra-type operators between~Zygmund~ type spaces
• The essential norm of a composition operator on the minimal Mobius invariant space
• Volterra-composition operators on the weighted Bergman space with exponential type weights
• Nuclear Volterra composition operators between Bloch and weighted type spaces