On the growth of the optimal constants of the multilinear Bohnenblust–Hille inequality
On the growth of the optimal constants of the multilinear Bohnenblust–Hille inequality
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多线性Bohnenblust-Hille不等式最优常数的增长
DOI：
10.1016/j.laa.2013.06.017
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发表时间：
2012
影响因子：
1.1
通讯作者：
D. Pellegrino
中科院分区：
文献类型：
--
作者：
D. Nunez;D. Pellegrino
设(Kn)n=1∞是满足多线性(实数或复数)Bohnenblust-Hille不等式的最优常数。80年前，随着Bohnenblust和Hille的论文发表在《数学年鉴》上，常量Kn的精确值仍有待发现。最近证明了(Kn)n=1∞具有次多项式增长性。此外，现在已知，如果存在L∈[−∞，∞]使得Lim n→∞(K n−K n−1)=L，则L=0。证明了如果存在一个L∈[0，∞]使得Lim n→∞K2 n Kn=L，则L∈[1，D]，其中D=e 1 2−1 2γ，D=e 1−1 2γ2(这里γ是著名的欧拉-马斯切罗尼常数).我们证明了这一结果推广了前者。
Abstract Let (K n) n= 1∞ be the optimal constants satisfying the multilinear (real or complex) Bohnenblust–Hille inequality. The exact values of the constants K n are still waiting to be discovered since eighty years ago, with the publication of Bohnenblust and Hille paper in the Annals of Mathematics. Recently, it was proved that (K n) n= 1∞ has a subpolynomial growth. Moreover it is now known that if there is an L∈[−∞,∞] such that lim n→∞(K n− K n− 1)= L, then L= 0. In this note we show that if there is an L∈[0,∞] such that lim n→∞ K 2 n K n= L, then L∈[1, D], with D= e 1 2− 1 2 γ for real scalars and D= e 1− 1 2 γ 2 for complex scalars (here γ is the famous Euler–Mascheroni constant). We show that this result generalizes the former.
影响因子：
1.3
作者：
Montanaro A
通讯作者：
Montanaro A