2020/03/28 by Fritz Gesztesy, Lance L. Littlejohn, Gesztesy, Fritz +5
Engineering · Social Sciences · #34A40 #35A23 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Labour Market and Migration #Mathematical Physics (math-ph) #Primary: 26D10 #Secondary: 34L10 #Spectral Theory (math.SP) #Structural Engineering and Materials Analysis
paper · pdf · doi:10.48550/arxiv.2003.12894
openalex publication_date 2020/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.