Analytic interpolation of certain multiplier spaces

Abstract

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 ^ V = 2. Let Us be the interpolation space [W2, Wi]β (see 1.1). Our main result, Theorem 2.4, states that for a compact subset E of the circle, U.\E= C(JE) if and only if W t\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 Us Φ Wp (see Theorem 2.7) for corresponding s and p. 1* Some properties of analytic interpolation*