2025/12/09 by Himadri Halder, Halder, Himadri · 1 citation
Mathematics · #31C10 #32A05 #46B07 #Advanced Banach Space Theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2512.09091
openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28
We study Bohr's theorem for vector valued holomorphic and operator valued pluriharmonic functions on complete Reinhardt domains in ℂn. Using invariants from local Banach space theory, we show that the associated Bohr radius is always strictly positive and obtain its asymptotic behavior separately in the finite- and infinite-dimensional settings. The framework developed here includes the classical Minkowski-space setting as a special case and applies to a wide class of Banach sequence spaces, including mixed Minkowski, Lorentz, and Orlicz spaces. We further establish a coefficient-type Schwarz-Pick lemma for operator valued pluriharmonic maps on complete Reinhardt domains.