supported by National Natural Science Foundation of China (Grant No. 10971128);Shanghai Leading Academic Discipline Project (Grant No. S30104);Scientific Research and Innovation Project of Shanghai Municipal Education Commission (Grant No. 09ZZ94);Innovation Foundation of Shanghai University (Grant No. SHUCX080134)
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 ...