Vol. 32, No. 1, 1970

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Analytic interpolation of certain multiplier spaces

James D. Stafney

Vol. 32 (1970), No. 1, 241–248

Let Wp denote the space of all functions on the circle which are the uniform limit of a sequence of trigonometric polynomials which is bounded as a sequence of multipliers for lp,1 p 2. Let Us be the interpolation space [W2,W1]s (see 1.1). Our main result, Theorem 2.4, states that for a compact subset E of the circle, Us|E = C(E) if and only if WI|E = C(E). A major step in the proof is a maximum principle for interpolation, Theorem 1.7. We also give a direct proof that UsWp (see Theorem 2.7) for corresponding s and p.

Mathematical Subject Classification 2000
Primary: 42A18
Secondary: 46E35
Received: 26 August 1968
Published: 1 January 1970
James D. Stafney