A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements


الملخص بالإنكليزية

The principal aim of this paper is to extend Birmans sequence of integral inequalities originally obtained in 1961, and containing Hardys and Rellichs 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 Muller-Pfeiffer. The results obtained considerably improve on prior results in the literature.

تحميل البحث