Abstract
AbstractIn this paper, we establish discrete Hardy–Rellich inequalities on with and optimal constants, for any . As far as we are aware, these sharp inequalities are new for . Our approach is to use weighted equalities to get some sharp Hardy inequalities using shifting weights, then to settle the higher order cases by iteration. We provide also a new Hardy–Leray–type inequality on with the same constant as the continuous setting. Furthermore, the main ideas work also for general graphs or the setting.
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