In this work we study weighted Sobolev spaces in ℝn generated by the Lie algebra of vector fields (1 + \x\2)1/2∂xj, 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 Lq estimates for the solution of the homogeneous wave equation. For the inhomogeneous wave equation we generalize the weighted Strichartz estimate established in  and establish global existence result for the supercritical semilinear wave equation with non-compact small initial data in these weighted Sobolev spaces.
|Translated title of the contribution||Weighted Strichartz estimate for the wave equation *|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|Publication status||Published - 2000 Mar 1|
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