2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66635We consider a general class of sharp $L^p$ Hardy inequalities in $\R^N$ involving distance from a surface of general codimension $1\leq k\leq N$. We show that we can succesively improve them by adding to the right hand side a lower order term with optimal weight and best constant. This leads to an infinite series improvement of $L^p$ Hardy inequalities.16 pages, to appear in the Indiana Univ. Math. JAnalysis of PDEsSpectral Theory35J20 (Primary) 26D10, 46E35 (Secondary)text