A note on n-harmonic majorants
1986 ◽
Vol 34
(3)
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pp. 461-472
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Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.
1987 ◽
Vol 35
(3)
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pp. 471-479
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2006 ◽
Vol 2006
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pp. 1-9
1974 ◽
Vol 76
(3)
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pp. 511-513
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1983 ◽
Vol 26
(3)
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pp. 317-323
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Keyword(s):
Keyword(s):
2015 ◽
Vol 93
(2)
◽
pp. 260-271
Keyword(s):
Keyword(s):