2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75133In this paper,we will study the boundedness properties of commutator \[ C_{f}=[ f,Δ] \] acting from $\overset{.}{H}^{1}(\mathbb{R}^{d}) $ to $\overset{.}{H}^{-1}(\mathbb{R}^{d}) .$Analysis of PDEs35-xx ;31Bxxtext