In this Note we give a generalization of Hardy's theorem for the Dunkl transform on . More precisely, for all a>0, b>0 and p,q∈[1,+∞], we determine the measurable functions f such that and , where are the Lp spaces associated with the Dunkl transform.
On donne dans cette Note une généralisation d'un théorème de Hardy pour la transformation de Dunkl sur . Plus précisément, pour toutes les valeurs de a>0, b>0 et p,q∈[1,+∞], on détermine les fonctions mesurables f telles que et , où les sont les espaces Lp associés à la transformation de Dunkl.
Accepted:
@article{CRMATH_2002__334_10_849_0, author = {Gallardo, L\'eonard and Trim\`eche, Khalifa}, title = {Un analogue d'un th\'eor\`eme de {Hardy} pour la transformation de {Dunkl}}, journal = {Comptes Rendus. Math\'ematique}, pages = {849--854}, publisher = {Elsevier}, volume = {334}, number = {10}, year = {2002}, doi = {10.1016/S1631-073X(02)02361-0}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02361-0/} }
TY - JOUR AU - Gallardo, Léonard AU - Trimèche, Khalifa TI - Un analogue d'un théorème de Hardy pour la transformation de Dunkl JO - Comptes Rendus. Mathématique PY - 2002 SP - 849 EP - 854 VL - 334 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02361-0/ DO - 10.1016/S1631-073X(02)02361-0 LA - fr ID - CRMATH_2002__334_10_849_0 ER -
%0 Journal Article %A Gallardo, Léonard %A Trimèche, Khalifa %T Un analogue d'un théorème de Hardy pour la transformation de Dunkl %J Comptes Rendus. Mathématique %D 2002 %P 849-854 %V 334 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02361-0/ %R 10.1016/S1631-073X(02)02361-0 %G fr %F CRMATH_2002__334_10_849_0
Gallardo, Léonard; Trimèche, Khalifa. Un analogue d'un théorème de Hardy pour la transformation de Dunkl. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 849-854. doi : 10.1016/S1631-073X(02)02361-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)02361-0/
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