Annales Mathématiques
Blaise Pascal
no. 2
Necessary condition for measures which are (L q ,L p ) multipliers
Bérenger Akon Kpata1 ; Ibrahim Fofana1 ; Konin Koua1
1 UFR Mathématiques et Informatique Université de Cocody 22 BP 582 Abidjan 22 Côte d’Ivoire
Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 339-353.

Soit G un groupe localement compact et ρ la mesure de Haar à gauche sur G. Etant donné une mesure de Radon positive μ, nous établissons une condition nécessaire sur les couples q,p pour lesquels μ est un multiplicateur de L q G,ρ dans L p G,ρ. Appliqué à ℝ n , notre résultat est plus fort que la condition nécessaire établie par Oberlin dans [14] et est très lié à une classe de mesures définie par Fofana dans [7].

Lorsque G est le tore, nous obtenons une généralisation d’une condition énoncée par Oberlin [15] et l’améliorons dans certains cas.

Let G be a locally compact group and ρ the left Haar measure on G. Given a non-negative Radon measure μ, we establish a necessary condition on the pairs q,p for which μ is a multiplier from L q G,ρ to L p G,ρ. Applied to ℝ n , our result is stronger than the necessary condition established by Oberlin in [14] and is closely related to a class of measures defined by Fofana in [7].

When G is the circle group, we obtain a generalization of a condition stated by Oberlin [15] and improve on it in some cases.

DOI : 10.5802/ambp.271
Classification : 43A05, 43A15
Keywords: Cantor-Lebesgue measure, $L^{q}$-improving measure, non-negative Radon measure
Mots clés : Mesure de Cantor-Lebesgue, mesure $L^{q}$-improving, mesure de Radon positive
Bérenger Akon Kpata 1 ; Ibrahim Fofana 1 ; Konin Koua 1

1 UFR Mathématiques et Informatique Université de Cocody 22 BP 582 Abidjan 22 Côte d’Ivoire 
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Bérenger Akon Kpata; Ibrahim Fofana; Konin Koua. Necessary condition for measures which are $(L^{q},L^{p})$ multipliers. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 339-353. doi : 10.5802/ambp.271. https://ambp.centre-mersenne.org/articles/10.5802/ambp.271/

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