Une estimation de Strichartz avec poids pour l'équation des ondes

In this work we study weighted Sobolev spaces in ℝn generated by the Lie algebra of vector fields (1 + \x\²)^1/2∂x_j, j = 1,...,n. Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in ℝⁿ. 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.