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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 .

Multipliers and linear functionals for the class 𝑁⁺