In this Note, we study some properties of the div, curl, grad operators and elliptic problems in the half-space. We consider data in weighted Sobolev spaces and in L1. © 2011 Elsevier Ltd. All rights reserved.245697702Amrouche, C., Girault, V., Giroire, J., Weighted Sobolev spaces for the Laplace equation in Rn (1994) Journal de Mathematiques Pures et Appliquees, 73 (6), pp. 579-606Bourgain, J., Brzis, H., On the equation div Y=f and application to control of phases (2002) Journal of the American Mathematical Society, 16 (2), pp. 393-426Bourgain, J., Brzis, H., New estimates for elliptic equations and Hodge type systems (2007) Journal of the European Mathematical Society, 9 (2), pp. 277-315Brzis, H., Schaftingen, J.V., Boundary estimates for elliptic systems with L1-data (2007) Calculus of Variations and Partial Differential Equations, 30 (3), pp. 369-388Amrouche, C., Neasov, S., Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition (2001) Acta Mathematica Scientia, 126 (2), pp. 265-274Van Schaftingen, J., Estimates for L1-vector fields (2004) Comptes Rendus de l'Acadmie des Sciences. Srie i, 339, pp. 181-186Girault, V., The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of R3 (1992) Journal of the Faculty of Science, the University of Tokyo, Section IA, 39 (2), pp. 279-307Amrouche, C., The Neumann problem in the half-space (2002) Comptes Rendus de l'Acadmie des Sciences. Srie i, 335, pp. 151-156