Sharp Weighted Discrete p-Hardy Inequality and Its Stability
A sharp weighted p-Hardy inequality is proved on the discrete half-line with power weights n^alpha for every real p>1. Extending Miclo's p=2 result and Muckenhoupt's continuous characterization, the work gives a quantitative criterion, in terms of two measures mu and nu on the discrete half-line, for a discrete p-Hardy inequality to hold, identifies the sharp constant, compares it against the constant in the continuous setting, and establishes a stability (quantitative deficit) version of the discrete inequality.
2501.00299
Pure-mathematics primary-research paper in functional analysis / spectral theory (Ali Barki, 26 pages). The author proves a sharp weighted p-Hardy inequality on the discrete half-line with power weig…