Abstract Given a bounded open subset Ω and closed subsets A, B of Rᵏ R k, we discuss when an estimate u (x) g (dist (x, A B) ) u (x) ≤ g (dist (x, A ∪ B) ), x (A B) x ∈ Ω \ (A ∪ B), for a function u subharmonic on B Ω \ B, implies that u (x) h (dist (x, B) ) u (x) ≤ h (dist (x, B) ), x B x ∈ Ω \ B, where g, h: (0, ) (0, ) g, h: (0, ∞) → (0, ∞) are decreasing functions and g (0^+) =h (0^+) = 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.
Bello et al. (Tue,) studied this question.