2025/08/06 by Bello, Glenier, Yakubovich, Dmitry
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2508.04496
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 (On the existence of a largest subharmonic minorant of a given function, Ark. Mat., 3 (1957), pp. 429-440) permits one to deduce other results in this direction. Then we compare these two approaches. Similar results are deduced for estimates of analytic functions.