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Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). (English) Zbl 0853.35062

Klainerman’s and Machedon’s remark gives the estimates of a solution to the homogeneous wave equation (in \(\mathbb{R}^{n+ 1}\)) in special norms, requiring less \(H^*\) differentiability of the initial data than \(H^{1/2}\) and \(H^{- 1/2}\). Tataru’s appendix provides an alternate approach for the proof of the same results in a more general framework. J. Bourgain gives another proof of one part of the above results.

MSC:

35L05 Wave equation
35B45 A priori estimates in context of PDEs
35L15 Initial value problems for second-order hyperbolic equations
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