On modules of the Hardy space of Hartogs triangle

2025/08/06 by Chattopadhyay, Arup, Giri, Saikat, Jain, Shubham
#30H10 #32H10 #32Q02 #47A15 #47A20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.04437

Abstract

In this paper, we investigate the structure of doubly commuting submodules and quotient modules of the Hardy space H²(\triangle_H) over the Hartogs triangle. We establish a complete classification of doubly commuting submodules. In addition, we characterize all doubly commuting quotient modules of the form (θ₁(z/w)θ₂(w)H²(\triangle_H))^⊥, where θ₁ and θ₂ are inner functions on the unit disc. This is achieved by introducing the concept of φ-doubly commuting quotient modules on the Hardy space H²(\mathbb D²). We further explore the essential normality and doubly commutativity of quotient modules of the form (pH²(\triangle_H))^⊥ under some mild assumptions on p, where p is a polynomial in two variables.

Citations

• Toeplitz operators on the n-dimensional Hartogs triangle
• Operator theory on generalized Hartogs triangles
• Holomorphic function spaces on the Hartogs triangle
• Pairs of commuting isometries - I
• Jordan Blocks of H²(Dⁿ)
• On two problems concerning linear transformations in hilbert space

Related

• Jordan Blocks of H²(Dⁿ)
• Submodules of the Hardy module over polydisc
• On Quotient modules of H²(\mathbbDⁿ): Essential Normality and Boundary Representations
• N_\p-type quotient modules on the torus
• Beurling quotient modules on the polydisc