Soit un groupe localement compact et la mesure de Haar à gauche sur . Etant donné une mesure de Radon positive , nous établissons une condition nécessaire sur les couples pour lesquels est un multiplicateur de dans . Appliqué à , 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 est le tore, nous obtenons une généralisation d’une condition énoncée par Oberlin [15] et l’améliorons dans certains cas.
Let be a locally compact group and the left Haar measure on . Given a non-negative Radon measure , we establish a necessary condition on the pairs for which is a multiplier from to . Applied to , 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 is the circle group, we obtain a generalization of a condition stated by Oberlin [15] and improve on it in some cases.
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
@article{AMBP_2009__16_2_339_0, author = {Kpata, B\'erenger Akon and Fofana, Ibrahim and Koua, Konin}, title = {Necessary condition for measures which are $(L^{q},L^{p})$ multipliers}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {339--353}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {16}, number = {2}, year = {2009}, doi = {10.5802/ambp.271}, zbl = {1178.43001}, mrnumber = {2568870}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.271/} }
TY - JOUR AU - Kpata, Bérenger Akon AU - Fofana, Ibrahim AU - Koua, Konin TI - Necessary condition for measures which are $(L^{q},L^{p})$ multipliers JO - Annales mathématiques Blaise Pascal PY - 2009 SP - 339 EP - 353 VL - 16 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.271/ DO - 10.5802/ambp.271 LA - en ID - AMBP_2009__16_2_339_0 ER -
%0 Journal Article %A Kpata, Bérenger Akon %A Fofana, Ibrahim %A Koua, Konin %T Necessary condition for measures which are $(L^{q},L^{p})$ multipliers %J Annales mathématiques Blaise Pascal %D 2009 %P 339-353 %V 16 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.271/ %R 10.5802/ambp.271 %G en %F AMBP_2009__16_2_339_0
Kpata, Bérenger Akon; Fofana, Ibrahim; Koua, Konin. 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. http://www.numdam.org/articles/10.5802/ambp.271/
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