Self-improving estimates of growth of subharmonic and analytic functions

Bello, Glenier (Universidad de Zaragoza) ; Yakubovich, Dmitry

Resumen: Given a bounded open subset Ω and closed subsets A, B of Rk, we discuss when an estimate u(x) ≤ g(dist(x, A ∪ B)), x ∈ Ω \ (A ∪ B), for a function u subharmonic on Ω\B, implies that u(x) ≤ h(dist(x, B)), x ∈ Ω \ B, where g, h : (0, ∞) → (0, ∞) are decreasing functions and g(0+) = h(0+) = ∞. We seek for explicit expressions of h in terms of g. We give some results of this type and show that Domar’s work Domar, Y Ark. Mat. 3, 429–440 (1957) permits one to deduce other results in this direction. Then we compare these two approaches. Similar results are deduced for estimates of analytic functions.

Idioma: Inglés

DOI: 10.1007/s00025-026-02606-7

Año: 2026

Publicado en: Results in Mathematics 81, 2 (2026), [25 pp.]
ISSN: 1422-6383

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-138342NB-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)