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Critical discrete Hardy inequalities in Lp
Abstract
We establish ground-state representations and critical Hardy inequalities in the discrete Lp setting. In particular, we construct critical Hardy weights for the discrete Dirichlet Laplacian on the half-line and the discrete fractional Laplacian on the integers for all p∈(1,∞). Our approach uses Sobolev--Bregman forms, for which the ground-state representations are exact identities and the corresponding Hardy weights are expressed through linear operators acting on powers of positive superharmonic functions.
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BibTeX
@misc{bogdan2026critical,
title = {{Critical discrete Hardy inequalities in $L^p$}},
author = {Krzysztof Bogdan and Shubham Gupta and Kamil Kaleta and Antoni Szczukiewicz},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30551},
eprint = {2608.30551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30551},
}
RIS
TY - UNPB
TI - Critical discrete Hardy inequalities in L^p
AU - Krzysztof Bogdan
AU - Shubham Gupta
AU - Kamil Kaleta
AU - Antoni Szczukiewicz
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30551
UR - https://arxiv.org/abs/2608.30551
AB - We establish ground-state representations and critical Hardy inequalities in the discrete L^p setting. In particular, we construct critical Hardy weights for the discrete Dirichlet Laplacian on the half-line and the discrete fractional Laplacian on the integers for all p∈(1,∞). Our approach uses Sobolev--Bregman forms, for which the ground-state representations are exact identities and the corresponding Hardy weights are expressed through linear operators acting on powers of positive superharmonic functions.
ER -