On a conjecture of Z. Jianzhong
1992 ◽
Vol 45
(1)
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pp. 163-170
Keyword(s):
Let ϕ be a nonnegative, nondecreasing and nonconstant function defined on [0, ∞) such that Φ(t) = ϕ(et) is a convex function on (-∞, ∞). The Hardy-Orlicz space H (ϕ) is defined to be the class of all those functions f holomorphic in the open unit disc of the complex plane C satisfying The subclass H(ϕ)+ of H(ϕ) is defined to be the class of all those functions f ∈ H(ϕ) satisfying for almost all points eit of the unit circle. In 1990, Z. Jianzhong conjectured that H(ϕ)+ = H(ψ)+ if and only if H(ϕ) = H(ψ). In the present paper we prove that it is true not only on the unit disc of C but also on the unit ball of Cn.
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1957 ◽
Vol 9
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pp. 426-434
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1986 ◽
Vol 100
(2)
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pp. 371-381
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1972 ◽
Vol 46
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pp. 111-120
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1995 ◽
Vol 117
(3)
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pp. 513-523
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1970 ◽
Vol 22
(2)
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pp. 342-347
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1986 ◽
Vol 99
(1)
◽
pp. 123-133
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