On the Lp norm of spectral clusters for compact manifolds with boundary

Acta Mathematica

Volumn 198, Issue 1, 2007, Pages 107-153

  Smith, Hart F ^a   Sogge, Christopher D ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247112472     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11511-007-0014-z     Document Type: Article

References (20)

1. CALDERÓN, A. P., Commutators of singular integral operators. Proc. Nat. Acad. Sci. U.S.A., 53 (1965), 1092-1099.
2. COIFMAN, R. & MEYER, Y., Commutateurs d'intégrales singulières et opérateurs multiliné aires. Ann. Inst. Fourier (Grenoble), 28:3 (1978), xi, 177-202.
3. CÓRDOBA, A. & FEFFERMAN, C., Wave packets and Fourier integral operators. Comm. Partial Differential Equations, 3 (1978), 979-1005.
4. DELEEUW, K. Unpublished, 1967.
5. p Bounds for Eigenfunctions and Spectral Projections of the Laplacian near Concave Boundaries. Ph.D. Thesis, UCLA, Los Angeles, CA, 1992.
6. _Uniform bounds for eigenfunctions of the Laplacian on manifolds with boundary. Comm. Partial Differential Equations, 27 (2002), 1283-1299.
7. KOCH, H. & TATARU, D., Dispersive estimates for principally normal pseudodifferential operators. Comm. Pure Appl. Math., 58 (2005), 217-284.
8. MOCKENHAUPT, G., SEEGER, A. & SOGGE, C. D., Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. J. Amer. Math. Soc., 6 (1993), 65-130.
9. RAYLEIGH, J. W., The problem of the whispering gallery. Philos. Mag., 20 (1920), 1001-1004.
10. RAYLEIGH, J. W. & STRUTT, B., The Theory of Sound. Dover, New York, NY, 1945.
11. 11 metrics. Amer. J. Math., 128 (2006), 1069-1103.
12. q bounds on spectral projectors for low regularity metrics. Math. Res. Lett., 13 (2006), 967-974.
13. SMITH, H. F. & SOGGE, C. D., On the critical semilinear wave equation outside convex obstacles. J. Amer. Math. Soc., 8 (1995), 879-916.
14. p norm of spectral clusters for second-order elliptic operators on compact manifolds. J. Funct. Anal., 77 (1988), 123-138.
15. _Fourier Integrals in Classical Analysis. Cambridge Tracts in Mathematics, 105. Cambridge University Press, Cambridge, 1993.
16. _Eigenfunction and Bochner Riesz estimates on manifolds with boundary. Math. Res. Lett., 9 (2002), 205-216.
17. STEIN, E. M. Unpublished, 1967.
18. TATARU, D., Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation. Amer. J. Math., 122 (2000), 349-376.
19. _Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. III. J. Amer. Math. Soc., 15 (2002), 419-442.
20. TAYLOR, M. E., Pseudodifferential Operators and Nonlinear PDE. Progress in Mathematics, 100. Birkhäuser, Boston, MA, 1991.