Analytic interpolation of certain multiplier spaces

James D. Stafney

Vol. 32 (1970), No. 1, 241–248

DOI: 10.2140/pjm.1970.32.241

Abstract

Let W_p 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 l_p,1 ≦ p ≦ 2. Let U_s 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, U_s|E = C(E) if and only if W_I|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 U_s≠W_p (see Theorem 2.7) for corresponding s and p.

Mathematical Subject Classification 2000

Primary: 42A18

Secondary: 46E35

Milestones

Received: 26 August 1968

Published: 1 January 1970