Radial behavior of positive harmonic Bloch functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 105-112
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Let $u$ be a strictly positive harmonic Bloch function on the upper half-space ${\mathbb R}_+^{d+1}$. Then the set
$$
\left\{x\in{\mathbb R}^d:\ \limsup_{y\to 0+}|{\log u(x, y)}|\infty\right\}
$$
has the maximal Hausdorff dimension.
@article{ZNSL_2007_345_a5,
author = {E. Doubtsov},
title = {Radial behavior of positive harmonic {Bloch} functions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {105--112},
publisher = {mathdoc},
volume = {345},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a5/}
}
E. Doubtsov. Radial behavior of positive harmonic Bloch functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 105-112. http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a5/