Geodesic
Multidimensional Opial inequalities for functions vanishing at an interior point
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 1, pp. 5-15

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In this paper we generalize Opial inequalities in the multidimensional case over balls. The inequalities carry weights and are proved to be sharp. The functions under consideration vanish at the center of the ball. 
Anastassiou, George A.; Goldstein, Gisèle Ruiz; Goldstein, Jerome A. Multidimensional Opial inequalities for functions vanishing at an interior point. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 1, pp. 5-15. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_1_a0/
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     author = {Anastassiou, George A. and Goldstein, Gis\`ele Ruiz and Goldstein, Jerome A.},
     title = {Multidimensional {Opial} inequalities for functions vanishing at an interior point},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {5--15},
     year = {2004},
     volume = {Ser. 9, 15},
     number = {1},
     zbl = {1072.26006},
     mrnumber = {MR2102751},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_1_a0/}
}
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