$p$在一定区间上的对称多项式和$l^p$不等式
Symmetric polynomials and $l^p$ inequalities for certain intervals of $p$
摘要：
本文证明了在一定的正实区间上，向量$ x, y \in [0,\infty)^n$和向量$p$的$l^p$不等式为$||x||_p \leq ||y||_p$形式的充分条件.我们的充分条件严格弱于通常的优化关系。这些条件用向量项中的某些齐次对称多项式表示。这些多项式包括作为特殊情况的初等对称多项式。利用对称多项式给出了优控关系的一个刻画。
英文摘要：
We prove some sufficient conditions implying $l^p$ inequalities of the form $||x||_p \leq ||y||_p$ for vectors $ x, y \in [0,\infty)^n$ and for $p$ in certain positive real intervals. Our sufficient conditions are strictly weaker than the usual majorization relation. The conditions are expressed in terms of certain homogeneous symmetric polynomials in the entries of the vectors. These polynomials include the elementary symmetric polynomials as a special case. We also give a characterization of the majorization relation by means of symmetric polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
