In this work we study weighted Sobolev spaces in R-n generated by the Lie algebra of vector fields (1 + x(2))(1/2)partial derivative(xj), j = 1,.,n. Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in R-n. As an application we derive weighted L-q estimates for the solution of the homogeneous wave equation. For the inhomogeneous wave equation we generalize the weighted Strichartz estimate established in [6] and establish global existence result for the supercritical semilinear wave equation with non-compact small initial data in these weighted Sobolev spaces. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.