On a theorem of Cartwright in higher dimensions

A. Logunov, E. Malinnikova, P. Mozolyako

Research output: Contribution to journalArticle

Abstract

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 languageEnglish (US)
Pages (from-to)65-82
Number of pages18
JournalJournal of the London Mathematical Society
Volume93
Issue number1
DOIs
StatePublished - Mar 9 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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