An improved discrete Rellich inequality on the half-line

Borbala Gerhat; David Krejcirik; Frantisek Stampach

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

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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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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.

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