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Fefferman’s SAK principle and a priori estimates for second order operators

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Abstract

We prove in details the higher codimensional version of Theorem 1.1 [11]. This provides a complete proof of Fefferman’s SAK Principle for a class of PDO’s with symplectic characteristic manifold.

Keywords: A priori estimates, General theory of PDO’s

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References

  • 1. Beals, R., Fefferman, C.L.: On local solvability of linear partial differential equations. Ann. of Math. 97, 482-498 (1974)

    Google Scholar 

  • 2. Boutet de Monvel, L., Grigis, A., Helffer, B.: Paramétrixes d'opérateurs pseudo-différentiels à caractéristiques multiples. Astérisque 34-35, 93-121 (1976)

    Google Scholar 

  • 3. Fefferman, C.L., Phong, D.H.: On positivity of pseudo-differential operators. Proc. Nat. Acad. Sci. 75, 4673-4674 (1978)

    Google Scholar 

  • 4. Fefferman, C.L.: The Uncertainty Principle. Bull. A.M.S. 9, 129-206 (1983)

  • 5. Fujiwara, D.: A construction of approximate positive parts of essentially selfadjoint pseudo-differential operators. Commun. Pure Appl. Math. 37, 101-147 (1984)

    Google Scholar 

  • 6. Hérau, F.: Fefferman's SAK principle in one dimension. Ann. Inst. Fourier 50, no. 4, 1229-1264 (2000)

  • 7. Hörmander, L.: The Cauchy problem for differential equations with double characteristics. J. d'Analyse Mathématique 32, 118-196 (1977)

  • 8. Hörmander, L.: The Analysis of Linear Partial Differential Operators, Vol. III and Vol. IV. Springer-Verlag, Berlin-Heidelberg (1983/85)

  • 9. Lerner, N., Nourrigat, J.: Lower bounds for pseudo-differential operators. Ann. Inst. Fourier 40, no. 3, 657-682 (1990)

    Google Scholar 

  • 10. Maniccia, L., Mughetti, M.: SAK principle for a class of Grushin-type operators. Revista Matemática Iberoamericana 22, no. 1, 259-286 (2006)

    Google Scholar 

  • 11. Maniccia, L., Mughetti, M.: A priori estimates for second order operators with symplectic characteristic manifold. To appear on Transactions of the American Mathematical Society (2006)

  • 12. Mustapha, S.: Sous ellipticité dans le cadre du calcul S(m,g). Comm. Partial Differential Equations 19, no. 1-2, 245-275 (1994)

  • 13. Mustapha, S.: Sous-ellipticité dans le cadre du calcul S(m,g). II. Comm. Partial Differential Equations 20, no. 3-4, 541-566 (1995)

  • 14. Parmeggiani, A.: A Class of counterexamples to the Fefferman-Phong Inequality for systems. Comm. in Partial Differential Equations 29, no. 9-10, 1281-1303 (2004)

  • 15. Parmeggiani, A.: Subunit balls for symbols of pseudodifferential operators. Adv. Math. 131, no. 2, 357-452 (1997)

  • 16. Tataru, D.: On the Fefferman-Phong inequality and related problems. Comm. in Partial Differential Equations 27, no. 11-12, 2101-2138 (2002)

  • 17. Treves, F.: Introduction to Pseudodifferential and Fourier Integral Operators, Vol. II. Plenum Press (1980)

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Maniccia, L., Mughetti, M. Fefferman’s SAK principle and a priori estimates for second order operators. Ann. Univ. Ferrara 52, 337–352 (2006). https://doi.org/10.1007/s11565-006-0025-2

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  • DOI: https://doi.org/10.1007/s11565-006-0025-2

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