The paper gives simple dyadic-annulus proofs of discrete Hardy inequalities with power weights on Z^d for all p and d, and identifies the optimal exponents for the local case.
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Fractional and non-fractional Hardy inequality on a lattice $\Z^d$
The paper gives simple dyadic-annulus proofs of discrete Hardy inequalities with power weights on Z^d for all p and d, and identifies the optimal exponents for the local case.