We consider harmonic functions in the unit ball of Rn+1 that are unbounded near the boundary, but can be estimated from above by some (rapidly increasing) radial weight w. Our main result gives some conditions on w that guarantee the estimate from below on the harmonic function by a multiple of this weight. In dimension 2, this reverse estimate was first obtained by Cartwright for the case of the power weights, wp(z) = (1 - |z|)-p, p>1, and then generalized to a wide class of regular weights by a number of authors.
|Original language||English (US)|
|Number of pages||18|
|Journal||Journal of the London Mathematical Society|
|State||Published - Mar 9 2015|
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