2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170015New Hardy and Sobolev type inequalities involving $L^1$-norms of scalar and vector-valued functions in $\Bbb{R}^n$ are obtained. The work is related to some problems stated in the recent paper by Bourgain and Breziscorrected typosAnalysis of PDEsFunctional Analysis42B20Estimates for differential operators of vector analysis involving $L^1$-normtext