Multipliers and linear functionals for the class
Multipliers and linear functionals for the class
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该类的乘法器和线性泛函
DOI：
10.1090/s0002-9947-1973-0338382-x
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发表时间：
1973
影响因子：
1.3
通讯作者：
N. Yanagihara
中科院分区：
文献类型：
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作者：
N. Yanagihara
最近有几位作者研究了H类的乘子，参见杜伦的著作《H空间理论》，学术出版社，纽约，1970年。这里我们考虑单位圆上全纯函数类N的相应问题，使得lim r ~ 2 *log+|/（rei&）| d6 ~ [i log +| f（ei6）| dd y_.|我们的结果是：1. zV是Banach意义下的F-空间，其距离函数为Pif，g）a±-f* 7 T\ogil + \fielie）-giel 0）\）dd。2.一个复数列A =…AS是…V到H* 的乘子，q是固定的，0 < q < cm，当且仅当A = 0（exp [- Ci/cm]），c是正的常数。3.空间N上的一个连续线性泛函A表示为一个全纯函数g（z）= 2bz”，它满足对一个正的常数c满足θ = CXexp [- c/n]）.相反，这样的函数g（z）-2b z”定义了空间zV上的连续线性泛函。
Multipliers for the classes H are studied recently by several authors, see Duren's book, Theory of H spaces, Academic Press, New York, 1970. Here we consider corresponding problems for the class N of holomorphic functions in the unit disk such that lim r2*log+|/(rei&)\d6~ [^ log + \f(ei6) \ dd y_.J J U J 0 < oo. Our results are: 1. zV is an F-space in the sense of Banach with the distance function Pif,g)a±-f*7T\ogil + \fieie)-giei0)\)dd. 2. A complex sequence A = ¡A S is a multiplier for ¡V into H* for a fixed q, 0 < q < cm, if and only if A = 0(exp [— Ci/ñ]) for a positive constant c. 3. A continuous linear functional <A on the space N is represented by a holomorphic function g(z) =2b z" which satisfies 6 = CXexp [— c/n]) for a positive constant c. Conversely, such a function g(z) -2b z" defines a continuous linear functional on the space zV .