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Renormings of Lp(Lq)

Published online by Cambridge University Press:  01 January 1999

R. DEVILLE ,
R. GONZALO  and
J. A. JARAMILLO
R. DEVILLE
Affiliation:
Laboratoire de Mathématiques, Université Bordeaux I, 351, cours de la Libération, 33400 Talence, France; e-mail: deville@math.u-bordeaux.fr
R. GONZALO
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain; e-mail: raquel26@eucmax.sim.ucm.es and jaramil@eucmax.sim.ucm.es
J. A. JARAMILLO
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain; e-mail: raquel26@eucmax.sim.ucm.es and jaramil@eucmax.sim.ucm.es
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Abstract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 1 , January 1999 , pp. 155 - 169
Copyright
The Cambridge Philosophical Society 1999

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