L p estimates for the wave equation and applications
Journées équations aux dérivées partielles (1993), article no. 15, 12 p. 
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     year = {1993},
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Sogge, Christopher D. $L^p$ estimates for the wave equation and applications. Journées équations aux dérivées partielles (1993), article  no. 15, 12 p. http://archive.numdam.org/item/JEDP_1993____A15_0/

1. M. Beals, Lp boundedness of Fourier integrals, Mem. Amer. Math. Soc. 264 (1982). | Zbl

2. M. Beals and M. Bezard, Low regularity local solutions for field equations, preprint. | Zbl

3. J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85. | MR | Zbl

4. J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geometric and Funct. Anal. 1 (1991), 69-85. | MR | Zbl

5. J. Bourgain, A harmonic analysis approach to problems in nonlinear differential equations, preprint. | Zbl

6. M. Christ, Lectures on singular integral operators, C.B.M.S. Lecture Notes, no. 77, American Math. Soc., Providence, RI, 1990. | MR | Zbl

7. M. Christ and M. Weinstein, Dispersion of low-amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109. | MR | Zbl

8. D. Grieser, Lp bounds for eigenfunctions and spectral projections of the Laplacian near concave boundaries, Thesis, UCLA (1992).

9. M.G. Grillakis, Regularity for the wave equation with a critical nonlinearity, Comm. Pure and Appl. Math. 45 (1992), 749-774. | MR | Zbl

10. J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Math. J. 39 (1990), 229-248. | MR | Zbl

11. L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. | MR | Zbl

L. Hörmander, Non-linear hyperbolic differential equations, Lund lecture notes, 1988.

13. F. John, The ultrahyperbolic equation with 4 independent variables, Duke J. Math. 4 (1938), 300-322. | JFM | Zbl

14. J.-L. Journé, A. Soffer and C.D. Sogge, Decay estimates for Schrödinger operators, Comm. Pure and Appl. Math. 44 (1991), 573-604. | MR | Zbl

15. L. Kapitanski, Weak and yet weaker solutions of semilinear wave equations, Brown Univ. preprint. | Zbl

16. C.E. Kenig, A. Ruiz and C.D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-349. | MR | Zbl

17. S. Klainerman and M. Machedon, The null condition and global existence for nonlinear waves, Comm. Pure and Appl. Math. (to appear).

18. H. Lindblad, A sharp counter example to local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993) (to appear). | MR | Zbl

19. H. Lindblad and C.D. Sogge, Minimal regularity for local existence of solutions to for semilinear Lorentz-invariant wave equations, in preparation.

20. W. Littman, Lp → Lq estimates for singular integrals, Proc. Symp. Pure and Appl. Math., vol. 23, Amer. Math. Soc., 1973, pp. 479-481. | MR | Zbl

21. G. Mockenhaupt, A. Seeger and C. D. Sogge, Wave front sets, local smoothing and Bourgain's circular maximal theorem, Annals of Math. 136 (1992), 207-218. | MR | Zbl

22. G. Mockenhaupt, A. Seeger and C.D. Sogge, Local smoothing of Fourier integrals and Carleson-Sjölin estimates, J. Amer. Math. Soc. 6 (1993), 65-130. | MR | Zbl

23. J. Peral, Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114-145. | MR | Zbl

24. J. Rauch, The u5-Klein-Gordan equation, Nonlinear PDE's and applications, vol. 53, Pitman Research Notes in Math., pp. 335-364. | MR | Zbl

25. J. Shatah and M. Struwe, Regularity results for nonlinear wave equations, preprint. | Zbl

26. A. Seeger, C.D. Sogge and E.M. Stein, Regularity properties of Fourier integral operators, Annals of Math 134 (1991), 231-251. | MR | Zbl

27. H. Smith and C.D. Sogge, Lp regularity for the wave equation with strictly convex obstacles (to appear). | Zbl

28. C.D. Sogge, Uniqueness in Cauchy problems for hyperbolic differential operators, Trans. Amer. Math. Soc. 333 (1992), 821-833. | MR | Zbl

29. C.D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376. | MR | Zbl

30. C.D. Sogge, Fourier integrals in classical analysis, Cambridge Univ. Press, Cambridge, New York, 1993. | MR | Zbl

31. E.M. Stein, Harmonic analysis real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, 1993. | MR | Zbl

32. W. Strauss, Nonlinear wave equations, C.B.M.S. Lecture Notes, no. 73, American Math. Soc., Providence, RI, 1989. | MR | Zbl

33. R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218-235. | MR | Zbl

34. R. Strichartz, Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation, Duke Math. J. 44 (1977), 705-714. | MR | Zbl

35. M. Struwe, Semilinear wave equations, Bull. Amer. Math. Soc. 26 (1992), 53-85. | MR | Zbl