On , we prove the existence of sharp logarithmic Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. Any function f ∈ satisfies
Sur , on établi l'existence d'inégalités de Sobolev logarithmiques optimales pour les dérivées fractionnelles d'ordre supérieur. Soit s et α deux réels positifs. Pour toute fonction f ∈ , on établit l'inégalité suivante :
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@article{CRMATH_2005__340_3_205_0, author = {Cotsiolis, Athanase and Tavoularis, Nikolaos K.}, title = {On logarithmic {Sobolev} inequalities for higher order fractional derivatives}, journal = {Comptes Rendus. Math\'ematique}, pages = {205--208}, publisher = {Elsevier}, volume = {340}, number = {3}, year = {2005}, doi = {10.1016/j.crma.2004.11.030}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.11.030/} }
TY - JOUR AU - Cotsiolis, Athanase AU - Tavoularis, Nikolaos K. TI - On logarithmic Sobolev inequalities for higher order fractional derivatives JO - Comptes Rendus. Mathématique PY - 2005 SP - 205 EP - 208 VL - 340 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.11.030/ DO - 10.1016/j.crma.2004.11.030 LA - en ID - CRMATH_2005__340_3_205_0 ER -
%0 Journal Article %A Cotsiolis, Athanase %A Tavoularis, Nikolaos K. %T On logarithmic Sobolev inequalities for higher order fractional derivatives %J Comptes Rendus. Mathématique %D 2005 %P 205-208 %V 340 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.11.030/ %R 10.1016/j.crma.2004.11.030 %G en %F CRMATH_2005__340_3_205_0
Cotsiolis, Athanase; Tavoularis, Nikolaos K. On logarithmic Sobolev inequalities for higher order fractional derivatives. Comptes Rendus. Mathématique, Volume 340 (2005) no. 3, pp. 205-208. doi : 10.1016/j.crma.2004.11.030. http://archive.numdam.org/articles/10.1016/j.crma.2004.11.030/
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