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/