论文标题
一系列加权的Birman-Hardy-Rellich不平等，并进行对数改进
A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements
论文作者
论文摘要
本文的主要目的是将Birman最初在1961年获得的整体不平等序列延长，并包含Hardy's和Rellich的不平等作为特殊情况，以使其不平等的序列融合了侧面和震撼力的功率重量的序列。我们针对这种不平等的新的证明技术依赖于最初是由于Hartman和Müller-Pfeiffer引起的转换的组合。结果对文献的先前结果有了很大的改善。
The principal aim of this paper is to extend Birman's sequence of integral inequalities originally obtained in 1961, and containing Hardy's and Rellich's inequality as special cases, to a sequence of inequalities that incorporates power weights on either side and logarithmic refinements on the right-hand side of the inequality as well. Our new technique of proof for this sequence of inequalities relies on a combination of transforms originally due to Hartman and Müller-Pfeiffer. The results obtained considerably improve on prior results in the literature.
