Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.
In this paper, we establish the Brascamp-Lieb inequality for positive double John basis and its reverse. As their applications, we estimate the upper and lower bounds for the volume product of two unit balls with the ...In this paper, we establish the Brascamp-Lieb inequality for positive double John basis and its reverse. As their applications, we estimate the upper and lower bounds for the volume product of two unit balls with the given norms. Moreover, the Loomis-Whitney inequality for positive double John basis is obtained.展开更多
基金Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No.24667).
文摘Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.
基金supported by National Natural Science Foundation of China (Grant No. 10971128)Shanghai Leading Academic Discipline Project (Grant No. S30104)+1 种基金Scientific Research and Innovation Project of Shanghai Municipal Education Commission (Grant No. 09ZZ94)Innovation Foundation of Shanghai University (Grant No. SHUCX080134)
文摘In this paper, we establish the Brascamp-Lieb inequality for positive double John basis and its reverse. As their applications, we estimate the upper and lower bounds for the volume product of two unit balls with the given norms. Moreover, the Loomis-Whitney inequality for positive double John basis is obtained.
