We study norm convolution inequalities in Lebesgue and Lorentz spaces. First, we improve the well-known O'Neil's inequality for the convolution operators and prove corresponding estimate from below. Second, we obtain Young–O'Neil-type estimate in the Lorentz spaces for the limit value parameters, i.e., . Finally, similar estimates in the weighted Lorentz spaces are presented.
Nous étudions des inégalités de normes de convolutions dans les espaces de Lebesgue et de Lorentz. En premier lieu, nous améliorons l'inégalité bien connue de O'Neil sur les opérateurs de convolution et nous établissons une minoration. En second lieu, nous donnons une estimation du type de Young–O'Neil dans les espaces de Lorentz, à savoir . Enfin, nous présentons des estimations similaires dans les espaces de Lorentz à poids.
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@article{CRMATH_2009__347_23-24_1385_0, author = {Nursultanov, Erlan and Tikhonov, Sergey and Tleukhanova, Nazerke}, title = {Norm inequalities for convolution operators}, journal = {Comptes Rendus. Math\'ematique}, pages = {1385--1388}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.003}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.003/} }
TY - JOUR AU - Nursultanov, Erlan AU - Tikhonov, Sergey AU - Tleukhanova, Nazerke TI - Norm inequalities for convolution operators JO - Comptes Rendus. Mathématique PY - 2009 SP - 1385 EP - 1388 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.10.003/ DO - 10.1016/j.crma.2009.10.003 LA - en ID - CRMATH_2009__347_23-24_1385_0 ER -
%0 Journal Article %A Nursultanov, Erlan %A Tikhonov, Sergey %A Tleukhanova, Nazerke %T Norm inequalities for convolution operators %J Comptes Rendus. Mathématique %D 2009 %P 1385-1388 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.10.003/ %R 10.1016/j.crma.2009.10.003 %G en %F CRMATH_2009__347_23-24_1385_0
Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke. Norm inequalities for convolution operators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1385-1388. doi : 10.1016/j.crma.2009.10.003. http://www.numdam.org/articles/10.1016/j.crma.2009.10.003/
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