In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a ...In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a random permutation. We now consider a sequence in lp with 1 〈 p 〈 ∞, and a sequence in a Banach lattice X. Instead of normal multiplication, we consider the tensor product of lp and X. We show that in Wittstock injective tensor product, lp iX, and Fremlin projective tensor product, lp FX, the rearrangement inequality still exists.展开更多
文摘In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a random permutation. We now consider a sequence in lp with 1 〈 p 〈 ∞, and a sequence in a Banach lattice X. Instead of normal multiplication, we consider the tensor product of lp and X. We show that in Wittstock injective tensor product, lp iX, and Fremlin projective tensor product, lp FX, the rearrangement inequality still exists.
