Some results of Bourgain on the radial variation of harmonic functions in the disk are extended to the setting of harmonic functions in upper half-spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-1,
author = {Michael D. O'Neill},
title = {Vertical variation of harmonic functions in upper half-spaces},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {1-12},
zbl = {0973.31002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-1}
}
Michael D. O'Neill. Vertical variation of harmonic functions in upper half-spaces. Colloquium Mathematicae, Tome 89 (2001) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-1/