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

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arxiv 2003.12894 v2 pith:DEJOEMRH submitted 2020-03-28 math.CA math-phmath.MPmath.SP

Fritz Gesztesy , Lance L. Littlejohn , Isaac Michael , Michael M. H. Pang This is my paper · ORCID
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keywords inequalitiessequenceinequalitylogarithmicobtainedoriginallyrefinementsresults
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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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  1. Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors

    math.NA 2025-06 conditional novelty 7.0 of 10

    Grassmann interpolation via maximum-volume local coordinates is matrix-decomposition-free and preserves Euclidean asymptotic error orders.

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