Vol. 32, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Analytic interpolation of certain multiplier spaces

James D. Stafney

Vol. 32 (1970), No. 1, 241–248
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 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
Milestones
Received: 26 August 1968
Published: 1 January 1970
Authors
James D. Stafney