Phragmén-Lindelöf Theorems and p-harmonic Measures for Sets Near Low-dimensional Hyperplanes

We prove estimates of a p -harmonic measure, p ∈( n − m , ∞ ], for sets in R n which are close to an m -dimensional hyperplane Λ⊂ R n , m ∈[0, n −1]. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains Ω⊂ R n ∖Λ for p -subharmonic functions. Moreover, we give local and global growth estimates for p -harmonic functions, vanishing on sets in R n , which are close to an m -dimensional hyperplane.