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Maximal functions of multipliers on compact manifolds without boundary
1. | Korea Institute for Advanced Study School of Mathematics, Hoegiro 85, Dongdaemun-gu, Seoul 130-722, South Korea |
References:
[1] |
N. Burq, P. Gérard and N. Tzvetkov, Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces, Invent. Math., 159 (2005), 187-223.
doi: 10.1007/s00222-004-0388-x. |
[2] |
N. Burq, P. Gérard and N. Tzvetkov, The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds, Phase Space Analysis of Partial Differential Equations. Vol. I, 21-52, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004. |
[3] |
N. Burq, P. Gérard and N. Tzvetkov, Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds, Duke Math. J., 138 (2007), 445-486.
doi: 10.1215/S0012-7094-07-13834-1. |
[4] |
S. Y. A Chang, M. Wilson and T. Wolff, Some weighted norm inequalities concerning the Schrödinger operator, Comment. Math. Helv., 60 (1985), 217-246.
doi: 10.1007/BF02567411. |
[5] |
W. Choi, Maximal functions for multipliers on stratified groups, Math. Nachr., 10.1002/mana.201300305
doi: 10.1002/mana.201300305. |
[6] |
M. Christ, $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328 (1991), 73-81.
doi: 10.2307/2001877. |
[7] |
M. Christ, Lectures on Singular Integral Operators, CBMS Regional Conference Series in Mathematics, 77, 1990. |
[8] |
M. Christ, L. Grafakos, P. Honzik and A. Seeger, Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type, Math. Z., 249 (2005), 223-240. |
[9] |
C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math., 93 (1971), 107-115. |
[10] |
G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Mathematical Notes, 28 Princeton University Press.; University of Tokyo Press, 1982. |
[11] |
L. Grafakos, P. Honzik and A. Seeger, On maximal functions for Mikhlin-Hörmander multipliers, Adv in Math., 204 (2006), 363-378.
doi: 10.1016/j.aim.2005.05.010. |
[12] |
P. Honzík, Maximal functions of multilinear multipliers, Math. Res. Lett., 16 (2009), 995-1006.
doi: 10.4310/MRL.2009.v16.n6.a7. |
[13] |
P. Honzik, Maximal Marcinkiewicz multipliers, Ark. Mat., 52 (2014), 135-147.
doi: 10.1007/s11512-013-0189-9. |
[14] |
A. Hassell and M. Tacy, Semiclassical $L^p$ estimates of quasimodes on curved hypersurfaces, J. Geom. Anal., 22 (2012), 74-89.
doi: 10.1007/s12220-010-9191-7. |
[15] |
L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math., 104 (1960), 93-139. |
[16] |
G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana, 6 (1990), 141-154.
doi: 10.4171/RMI/100. |
[17] |
A. Seeger and C. D. Sogge, On the boundedness of functions of (pseudo-) differential operators on compact manifolds, Duke Math. J., 59 (1989), 709-736.
doi: 10.1215/S0012-7094-89-05932-2. |
[18] |
C. D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math., 126 (1987), 439-447.
doi: 10.2307/1971356. |
[19] |
C. D. Sogge, Fourier Integrals in Classical Analysis, Cambridge Tracts in Mathematics, 105. Cambridge University Press, Cambridge, 1993.
doi: 10.1017/CBO9780511530029. |
[20] |
M. Tacy, Semiclassical $L^p$ estimates of quasimodes on submanifolds, Comm. Partial Differential Equations, 35 (2010), 1538-1562.
doi: 10.1080/03605301003611006. |
[21] |
M. Taylor, Pseudo-differential Operators, Princeton Univ. Press, Princeton N.J., 1981. |
show all references
References:
[1] |
N. Burq, P. Gérard and N. Tzvetkov, Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces, Invent. Math., 159 (2005), 187-223.
doi: 10.1007/s00222-004-0388-x. |
[2] |
N. Burq, P. Gérard and N. Tzvetkov, The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds, Phase Space Analysis of Partial Differential Equations. Vol. I, 21-52, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004. |
[3] |
N. Burq, P. Gérard and N. Tzvetkov, Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds, Duke Math. J., 138 (2007), 445-486.
doi: 10.1215/S0012-7094-07-13834-1. |
[4] |
S. Y. A Chang, M. Wilson and T. Wolff, Some weighted norm inequalities concerning the Schrödinger operator, Comment. Math. Helv., 60 (1985), 217-246.
doi: 10.1007/BF02567411. |
[5] |
W. Choi, Maximal functions for multipliers on stratified groups, Math. Nachr., 10.1002/mana.201300305
doi: 10.1002/mana.201300305. |
[6] |
M. Christ, $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328 (1991), 73-81.
doi: 10.2307/2001877. |
[7] |
M. Christ, Lectures on Singular Integral Operators, CBMS Regional Conference Series in Mathematics, 77, 1990. |
[8] |
M. Christ, L. Grafakos, P. Honzik and A. Seeger, Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type, Math. Z., 249 (2005), 223-240. |
[9] |
C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math., 93 (1971), 107-115. |
[10] |
G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Mathematical Notes, 28 Princeton University Press.; University of Tokyo Press, 1982. |
[11] |
L. Grafakos, P. Honzik and A. Seeger, On maximal functions for Mikhlin-Hörmander multipliers, Adv in Math., 204 (2006), 363-378.
doi: 10.1016/j.aim.2005.05.010. |
[12] |
P. Honzík, Maximal functions of multilinear multipliers, Math. Res. Lett., 16 (2009), 995-1006.
doi: 10.4310/MRL.2009.v16.n6.a7. |
[13] |
P. Honzik, Maximal Marcinkiewicz multipliers, Ark. Mat., 52 (2014), 135-147.
doi: 10.1007/s11512-013-0189-9. |
[14] |
A. Hassell and M. Tacy, Semiclassical $L^p$ estimates of quasimodes on curved hypersurfaces, J. Geom. Anal., 22 (2012), 74-89.
doi: 10.1007/s12220-010-9191-7. |
[15] |
L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math., 104 (1960), 93-139. |
[16] |
G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana, 6 (1990), 141-154.
doi: 10.4171/RMI/100. |
[17] |
A. Seeger and C. D. Sogge, On the boundedness of functions of (pseudo-) differential operators on compact manifolds, Duke Math. J., 59 (1989), 709-736.
doi: 10.1215/S0012-7094-89-05932-2. |
[18] |
C. D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math., 126 (1987), 439-447.
doi: 10.2307/1971356. |
[19] |
C. D. Sogge, Fourier Integrals in Classical Analysis, Cambridge Tracts in Mathematics, 105. Cambridge University Press, Cambridge, 1993.
doi: 10.1017/CBO9780511530029. |
[20] |
M. Tacy, Semiclassical $L^p$ estimates of quasimodes on submanifolds, Comm. Partial Differential Equations, 35 (2010), 1538-1562.
doi: 10.1080/03605301003611006. |
[21] |
M. Taylor, Pseudo-differential Operators, Princeton Univ. Press, Princeton N.J., 1981. |
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