On some new embeddings in minimal bounded homogeneous domains in Cⁿ

2025/08/09 by Romi F. Shamoyan, Shamoyan, R. F., Natalia M. Makhina +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.07091

openalex publication_date 2025/08/09 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

In this short note we consider very general bounded minimal homogeneous domains. Under certain natural additional conditions new sharp results on Bergman type analytic spaces in minimal bounded homogeneous domains are obtained. Domains we consider here are direct generalizations of the well-studied so-called bounded symmetric domains in Cⁿ. In the unit disk and in the unit ball all our results were obtained by first author. Some results were obtained previously in tubular and bounded pseudoconvex domains. Our proofs are heavily based on properties of so called r-lattices for these general domains provided in recent papers of Yamaji. Our proofs are also based on arguments provided earlier in less general domains. We partially extend an embedding result from Yamaji's paper.

Citations

• Essential norm estimates for positive Toeplitz operators on the weighted Bergman space of a minimal bounded homogeneous domain
• Composition operators on the Bergman spaces of a minimal bounded homogeneous domain
• Some estimates of the Bergman kernel of minimal bounded homogeneous domains

Related

• On embedding theorems in analytic and harmonic function spaces of several variables in some domains in Cⁿ
• Some estimates of the Bergman kernel of minimal bounded homogeneous domains
• On Bergman projections and sharp decomposition theorems in tubular and related domains in Cⁿ
• New classes of domains with explicit Bergman kernel
• Examples of Unbounded Homogeneous Domains in Complex Space