Higher-order Volterra-type integral operator on Hardy and Bergman spaces

2025/12/18 by Kargar, Rahim
#47B01 #47B38 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.16412

Abstract

We investigate the higher-order Volterra-type integral operator T_g,n on the unit disk, defined for n∈\mathbb N by T_g,n[f](z) := \underbrace∫₀^z∫₀^t₁⋯∫₀^t_{n-1n times} f(t_n)g'(t_n) dt_n⋯ dt₁, z∈\mathbb D, where f and g are analytic in the unit disk \mathbb D. We establish sharp norm and essential norm estimates, and give complete characterizations of boundedness and compactness of T_g,n on Hardy spaces H^p and weighted Bergman spaces A_α^p, in terms of (vanishing) Carleson measure conditions determined by |g'|.

Citations

• Carleson-type embeddings with closed range
• On the boundedness of generalized integration operators on Hardy spaces
• Volterra type integral operator and analytic function spaces
• The Essential Norm of a Composition Operator
• Bounded Projections, Duality, and Multipliers in Spaces of Analytic Functions

Related

• Generalized Volterra type integral operators on large Bergman spaces
• Volterra type integration operators between weighted Bergman spaces and Hardy spaces
• Volterra type integration operators from Bergman spaces to Hardy spaces
• Volterra type integral operator and analytic function spaces
• Volterra-type operators mapping weighted Dirichlet space into H^∞