The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
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DOI：
10.4007/annals.2011.174.1.13
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发表时间：
2009-04
影响因子：
4.9
通讯作者：
A. Defant;L. Frerick;J. Ortega-Cerdà;M. Ounaies;K. Seip
中科院分区：
文献类型：
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作者：
A. Defant;L. Frerick;J. Ortega-Cerdà;M. Ounaies;K. Seip
Bohnenblust-Hille不等式认为Cn上的m-齐次多项式P的系数的'2 m+1 -范数有界于kPk 1乘以一个与n无关的常数，其中kk 1表示多圆盘Dn上的上确界范数.本文的主要结果是这个不等式是超压缩的，即，对于某些C > 1，该常数可以取为Cm。将这个改进的Bohnenblust-Hille不等式与其它结果相结合，我们得到：多圆盘Dn的Bohr半径渐近地表现为p（logn）=n模一个远离0和无穷大的因子，
The Bohnenblust-Hille inequality says that the ‘ 2m m+1 -norm of the coefcients of an m-homogeneous polynomial P on C n is bounded by kPk1 times a constant independent of n, wherekk 1 denotes the supremum norm on the polydisc D n . The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be C m for some C > 1. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc D n behaves asymptotically as p (logn)=n modulo a factor bounded away from 0 and innity,