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An improved discrete Rellich inequality on the half-line

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arxiv 2206.11007 v1 pith:2NAV5ONU submitted 2022-06-22 math.SP math.CA

Borbala Gerhat , David Krejcirik , Frantisek Stampach This is my paper · ORCID
classification math.SPmath.CA
keywords discreteimprovedinequalityrellichconjecturediscussfactorizationformulate
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Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the discrete Rellich inequality on the full space.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An optimal fractional Hardy inequality on the discrete half-line

    math.AP 2025-07 conditional novelty 6.0 of 10

    For σ in (0,1], the paper constructs an explicit optimal Hardy weight W^op_σ for (-Δ_N)^σ, with W^op_σ(n) approximately n^{-2σ} and an upper bound C_σ for the best constant in the n^{-2σ} Hardy inequality.

  2. Optimal Poincar\'e-Hardy-type Inequalities on Manifolds and Graphs

    math.AP 2025-01 conditional novelty 6.0 of 10

    The paper derives explicit optimal Poincaré-Hardy weights on weakly spherically symmetric graphs and shows they dominate Green's-function-based optimal weights at infinity.

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