论文标题
一维整数晶格的对称不平等现象
Symmetrization inequalities on one-dimensional integer lattice
论文作者
论文摘要
在本文中，我们在一个维整数晶格上发展了对称性的理论。更确切地说，我们将径向降低的函数$ u^*$与整数上定义的函数$ u $相关联，并证明相应的polya-szegö不平等。一路走来，我们还证明了加权的polya-szegö不平等，以减少半线（即非阴性整数）的重排。结果，我们证明了离散的加权Hardy的不平等，重量$ n^α$，价格为$ 1 <α\ leq 2 $。
In this paper, we develop a theory of symmetrization on the one dimensional integer lattice. More precisely, we associate a radially decreasing function $u^*$ with a function $u$ defined on the integers and prove the corresponding Polya-Szegö inequality. Along the way we also prove the weighted Polya-Szegö inequality for the decreasing rearrangement on the half-line, i.e., non-negative integers. As a consequence, we prove the discrete weighted Hardy's inequality with the weight $n^α$ for $1 < α\leq 2$.
