Characterisations for analytic functions of bounded mean oscillation
1992 ◽
Vol 46
(1)
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pp. 115-125
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Keyword(s):
Let α > 0 and let f[α](z) be the αth fractional derivative of an analytic function f on the unit disc D. In this paper we show that f ∈ BMOA if and only if |f[α](z)|2 (l - |z|2)2α−1dA(z) is a Carleson measure and f ∈ VMOA if and only if |f[α](z)|2 (1 − |z|2)2α−1dA(z) is a vanishing Carleson measure, where A denotes the normalised Lebesgue measure on D. Hence a significant extension of familiar characterisations for analytic functions of bounded and vanishing mean oscillation is obtained.
1984 ◽
Vol 36
(4)
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pp. 747-755
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2010 ◽
Vol 17
(3)
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pp. 529-542
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Keyword(s):
1999 ◽
Vol 42
(1)
◽
pp. 97-103
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Keyword(s):
Keyword(s):
1978 ◽
Vol 10
(2)
◽
pp. 219-224
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1998 ◽
Vol 47
(3)
◽
pp. 0-0
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1981 ◽
Vol s2-24
(2)
◽
pp. 243-254
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Keyword(s):