Mathematical Proceedings of the Cambridge Philosophical Society

Renormings of Lp(Lq)

R. DEVILLE a1, R. GONZALO a2 1 and J. A. JARAMILLO a2 1
a1 Laboratoire de Mathématiques, Université Bordeaux I, 351, cours de la Libération, 33400 Talence, France; e-mail:
a2 Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain; e-mail: and


We investigate the best order of smoothness of Lp(Lq). We prove in particular that there exists a [script C][infty infinity]-smooth bump function on Lp(Lq) if and only if p and q are even integers and p is a multiple of q.

(Received July 3 1997)
(Revised March 11 1998)


1 The research of the second and third authors was partially supported by DGICYT grant PB 93-0452.