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A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements (2003.12894v2)
Published 28 Mar 2020 in math.CA, math-ph, math.MP, and math.SP
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.
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