A Wiener algebra for the Fefferman-Phong inequality
Lerner, Nicolas1 ; Morimoto, Yoshinori2
1 Université de Rennes 1, Irmar, Campus de Beaulieu, 35042 Rennes cedex, France
2 Grad.School of Hum.&Environ. Studies, Kyoto University, Kyoto 606-8501, Japan
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 17, 10 p.
Lerner, Nicolas 1 ; Morimoto, Yoshinori 2

1 Université de Rennes 1, Irmar, Campus de Beaulieu, 35042 Rennes cedex, France
2 Grad.School of Hum.&Environ. Studies, Kyoto University, Kyoto 606-8501, Japan 
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Lerner, Nicolas; Morimoto, Yoshinori. A Wiener algebra for the Fefferman-Phong inequality. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 17, 10 p. http://www.numdam.org/item/SEDP_2005-2006____A17_0/

[AM] H.Ando, Y.Morimoto Wick calculus and the Cauchy problem for some dispersive equations, Osaka J. Math., Volume 39 (2002) no. 1, pp. 123-147 | MR | Zbl

[B1] Boulkhemair, A Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators, Math.Res.Lett., Volume 4 (1997), pp. 53-67 | MR | Zbl

[B2] Boulkhemair, A L 2 estimates for Weyl quantization, J.Func.Anal., Volume 165 (1999), pp. 173-204 | MR | Zbl

[Be] Berezin, F.A Quantization, Math.USSR, Izvest., Volume 8 (1974), pp. 1109-1165 | Zbl

[Bo1] Bony, J.-M Sur l’inégalité de Fefferman-Phong, Séminaire EDP, Ecole Polytechnique (1998-99) (Exposé 3)

[Bo2] Bony, J.-M Décomposition des fonctions positives en sommes de carrés, Journées Equations aux Dérivées Partielles (2004) (Exposé 3, Ecole Polytech., Palaiseau) | Numdam | MR | Zbl

[CF] Córdoba, A; Fefferman, C.L Wave packets and Fourier integral operators, Comm. Partial Differential Equations, Volume 3 (1978) no. 11, pp. 979-1005 | MR | Zbl

[FP] Fefferman, C; Phong, D.H On positivity of pseudo-differential equations, Proc.Nat.Acad.Sci., Volume 75 (1978), pp. 4673-4674 | MR | Zbl

[G0] Glaeser, G Racine carrée d’une fonction différentiable, Ann.Inst.Fourier, Volume 13 (1963) no. 2, pp. 203-210 | Numdam | Zbl

[GL] Gröchenig, K; Leinert, M Wiener’s lemma for twisted convolution and Gabor frames, J. Amer. Math. Soc., Volume 17 (2004) no. 1, pp. 1-18 | Zbl

[Gu] Guan, P C 2 A Priori Estimates for Degenerate Monge-Ampère Equations, Duke Math. J., Volume 86 (1997) no. 2, p. 323-346. | MR | Zbl

[H1] Hörmander, L The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math., Volume 32 (1979) no. 3, pp. 360-444 | MR | Zbl

[H2] Hörmander, L The analysis of linear partial differential operators I-IV, Springer Verlag, 1983-85 | Zbl

[He] Hérau, F Melin-Hörmander inequality in a Wiener type pseudo-differential algebra, Ark. Mat., Volume 39 (2001) no. 2, pp. 311-338 | MR | Zbl

[Ke] Kellogg, O.D On bounded polynomials in several variables, Math.Z., Volume 27 (1928), pp. 55-64 | MR

[Le] Lerner, N Energy methods via coherent states and advanced pseudo-differential calculus, Multidimensional complex analysis and partial differential equations, Contemporary Mathematics, 1997, pp. 177-201 | MR | Zbl

[LM] N.Lerner, Y.Morimoto On the Fefferman-Phong inequality and a Wiener-type algebra of pseudodifferential operators, preprint, 33 pages, http://perso.univ-rennes1.fr/nicolas.lerner/ (Feb.23, 2006) | MR

[S1] Sjöstrand, J An algebra of pseudodifferential operators, Math.Res.Lett., Volume 1 (1994), pp. 2, 189-192 | MR | Zbl

[S2] Sjöstrand, J Wiener type algebras of pseudodifferential operators, Séminaire EDP, École Polytechnique (1994-95) (Exposé 4) | Numdam | MR | Zbl

[Ta] Tataru, D On the Fefferman-Phong inequality and related problems, Comm. Partial Differential Equations, Volume 27 (2002) no. 11-12, pp. 2101-2138 | MR | Zbl

[Un] Unterberger, A Oscillateur harmonique et opérateurs pseudo-différentiels, Ann.Inst.Fourier, Volume 29 (1979) no. 3, pp. 201-221 | Numdam | MR | Zbl