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.
An improved discrete Rellich inequality on the half-line
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
An optimal fractional Hardy inequality on the discrete half-line
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.