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標題Title: ON A THEOREM OF M. CARTWRIGHT IN HIGHER DIMENSIONS
作者Authors: A. LOGUNOV, E. MALINNIKOVA, AND P. MOZOLYAKO
上傳單位Department: 電子工程系
上傳時間Date: 2016-6-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: harmonic functions
摘要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 two this reverse estimate was first obtained by M. 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.

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2016_6_798ca594.pdf 257Kb pdf 22 1
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