A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements
Classical Analysis and ODEs
2020-04-01 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
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 M\"uller-Pfeiffer. The results obtained considerably improve on prior results in the literature.
Keywords
Cite
@article{arxiv.2003.12894,
title = {A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements},
author = {Fritz Gesztesy and Lance L. Littlejohn and Isaac Michael and Michael M. H. Pang},
journal= {arXiv preprint arXiv:2003.12894},
year = {2020}
}
Comments
32 pages, typos removed