Self-improving estimates of growth of subharmonic and analytic functions
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 e...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Universidad Autónoma de Madrid |
| Repository: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Language: | English |
| OAI Identifier: | oai:repositorio.uam.es:10486/752881 |
| Online Access: | https://hdl.handle.net/10486/752881 https://dx.doi.org/10.1007/s00025-026-02606-7 |
| Access Level: | Open access |
| Keyword: | Subharmonic functions Estimates of subharmonic functions Estimates of analytic functions Boundary growth Matemáticas |
| Summary: | 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 |
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