Let Δ𝔹 be the Laplace–Beltrami operator associated with Bergman metric on the unit ball 𝔹 of ℂN. We estimate the nonisotropic Hausdorff dimension of a set in ∂𝔹 where a positive Δ𝔹-superharmonic function u satisfying -Δ𝔹u (z) ≤c (1-|z|) τu (z) p in 𝔹 for some p∈ (0, N/ (N-1) ), τ>maxα (p−1), N (p−1) and c>0 grows faster than a prescribed order α.
Kentaro Hirata (Thu,) studied this question.