L p estimates for the wave equation and applications
Journées équations aux dérivées partielles (1993), article no. 15, 12 p.
@article{JEDP_1993____A15_0,
     author = {Sogge, Christopher D.},
     title = {$L^p$ estimates for the wave equation and applications},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {15},
     publisher = {Ecole polytechnique},
     year = {1993},
     mrnumber = {94f:35076},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1993____A15_0/}
}
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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://www.numdam.org/item/JEDP_1993____A15_0/

1. M. Beals, Lp boundedness of Fourier integrals, Mem. Amer. Math. Soc. 264 (1982). | Zbl 0508.42020

2. M. Beals and M. Bezard, Low regularity local solutions for field equations, preprint. | Zbl 0852.35098

3. J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85. | MR 88f:42036 | Zbl 0626.42012

4. J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geometric and Funct. Anal. 1 (1991), 69-85. | MR 92g:42010 | Zbl 0756.42014

5. J. Bourgain, A harmonic analysis approach to problems in nonlinear differential equations, preprint. | Zbl 0822.35116

6. M. Christ, Lectures on singular integral operators, C.B.M.S. Lecture Notes, no. 77, American Math. Soc., Providence, RI, 1990. | MR 92f:42021 | Zbl 0745.42008

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 92h:35203 | Zbl 0743.35067

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 93e:35073 | Zbl 0785.35065

10. J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Math. J. 39 (1990), 229-248. | MR 91j:35158 | Zbl 0683.35008

11. L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. | MR 58 #29418 | Zbl 0164.13201

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 64.0497.04 | Zbl 0019.02404

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 93d:35034 | Zbl 0743.35008

15. L. Kapitanski, Weak and yet weaker solutions of semilinear wave equations, Brown Univ. preprint. | Zbl 0831.35109

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 88d:35037 | Zbl 0644.35012

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 94h:35165 | Zbl 0797.35123

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 50 #10909 | Zbl 0263.44006

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 93i:42009 | Zbl 0759.42016

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 93h:58150 | Zbl 0776.58037

23. J. Peral, Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114-145. | MR 81k:35089 | Zbl 0442.35017

24. J. Rauch, The u5-Klein-Gordan equation, Nonlinear PDE's and applications, vol. 53, Pitman Research Notes in Math., pp. 335-364. | MR 83a:35066 | Zbl 0473.35055

25. J. Shatah and M. Struwe, Regularity results for nonlinear wave equations, preprint. | Zbl 0836.35096

26. A. Seeger, C.D. Sogge and E.M. Stein, Regularity properties of Fourier integral operators, Annals of Math 134 (1991), 231-251. | MR 92g:35252 | Zbl 0754.58037

27. H. Smith and C.D. Sogge, Lp regularity for the wave equation with strictly convex obstacles (to appear). | Zbl 0805.35169

28. C.D. Sogge, Uniqueness in Cauchy problems for hyperbolic differential operators, Trans. Amer. Math. Soc. 333 (1992), 821-833. | MR 92m:35006 | Zbl 0763.35012

29. C.D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376. | MR 92i:58192 | Zbl 0754.35004

30. C.D. Sogge, Fourier integrals in classical analysis, Cambridge Univ. Press, Cambridge, New York, 1993. | MR 94c:35178 | Zbl 0783.35001

31. E.M. Stein, Harmonic analysis real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, 1993. | MR 95c:42002 | Zbl 0821.42001

32. W. Strauss, Nonlinear wave equations, C.B.M.S. Lecture Notes, no. 73, American Math. Soc., Providence, RI, 1989. | MR 91g:35002 | Zbl 0714.35003

33. R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218-235. | MR 41 #2231 | Zbl 0189.40701

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 58 #23577 | Zbl 0372.35001

35. M. Struwe, Semilinear wave equations, Bull. Amer. Math. Soc. 26 (1992), 53-85. | MR 92e:35112 | Zbl 0767.35045