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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

A priori estimates for second order operators with symplectic characteristic manifold

Author(s): Lidia Maniccia; Marco Mughetti
Journal: Trans. Amer. Math. Soc. 359 (2007), 5193-5206.
MSC (2000): Primary 35B45; Secondary 35S05
Posted: June 22, 2007
MathSciNet review: 2327027
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Abstract | References | Similar articles | Additional information

Abstract: We prove Fefferman's SAK Principle for a class of classical pseudodifferential operators on $ \mathbb{R}^n$ with symplectic characteristic manifold.


References:

1.
R.Beals, C.L.Fefferman: On local solvability of linear partial differential equations. Ann. of Math., 97, 482-498 (1974). MR 0352746 (50:5233)

2.
L.Boutet de Monvel, A.Grigis and B.Helffer: Paramétrixes d'opérateurs pseudo-différentiels à caractéristiques multiples. Astérisque, 34-35, 93-121 (1976). MR 0493005 (58:12046)

3.
C.L.Fefferman, D.H.Phong: On positivity of pseudo-differential operators. Proc. Nat. Acad. Sci., 75, 4673-4674 (1978).MR 0507931 (80b:47064)

4.
C.L.Fefferman: The Uncertainty Principle. Bull. A.M.S., 9, 129-206 (1983).MR 0707957 (85f:35001)

5.
D.Fujiwara: A construction of approximate positive parts of essentially selfadjoint pseudo-differential operators. Commun. Pure Appl. Math., 37, 101-147 (1984).MR 0728268 (85i:47051)

6.
F.Hérau: Fefferman's SAK principle in one dimension. Ann. Inst. Fourier, 50 (4), 1229-1264 (2000). MR 1799744 (2001k:35310)

7.
L.Hörmander: The Cauchy problem for differential equations with double characteristics. J. d'Analyse Mathématique, 32, 118-196, (1977).MR 0492751 (58:11822)

8.
L.Hörmander: The Analysis of Linear Partial Differential Operators, Vol. III and Vol. IV. Springer-Verlag (1983/85).MR 0781536 (87d:35002a); MR 0781537 (87d:35002b)

9.
R.Lascar: Propagation des singularites et hypoellipticite pour des operateurs pseudo-differentiels a caracteristiques doubles. Comm. in Partial Differential Equations, 3 (3), 201-247 (1978). MR 0492798 (58:11863)

10.
N.Lerner, J.Nourrigat: Lower bounds for pseudo-differential operators. Ann. Inst. Fourier, 40 (3), 657-682 (1990).MR 1091836 (92a:35172)

11.
L.Maniccia, M.Mughetti: SAK principle for a class of Grushin-type operators. Revista Matematicá Iberoamericana, 22 (1), 259-286 (2006). MR 2268119

12.
L.Maniccia, M.Mughetti: Fefferman's SAK principle and a priori estimates for second order operators. Ann. Univ. Ferrara Sez. VII Sci. Mat., 52, 337-352 (2007). MR 2273103

13.
S.Mustapha: Sous ellipticité dans le cadre du calcul $ S(m,g)$. Comm. Partial Differential Equations 19 (1-2), 245-275 (1994). MR 1257005 (95c:35279)

14.
S.Mustapha: Sous-ellipticité dans le cadre du calcul $ S(m,g)$. II. Comm. Partial Differential Equations 20 (3-4), 541-566 (1995).MR 1318080 (96a:35225)

15.
A.Parmeggiani: A Class of counterexamples to the Fefferman-Phong Inequality for systems. Comm. in Partial Differential Equations, 29 (9,10), 1281-1303 (2004).MR 2103837 (2005h:35385)

16.
A.Parmeggiani: Subunit balls for symbols of pseudodifferential operators. Adv. Math., 131(2), 357-452 (1997). MR 1483973 (99c:35270)

17.
D.Tataru: On the Fefferman-Phong inequality and related problems. Comm. in Partial Differential Equations, 27 (11,12), 2101-2138 (2002).MR 1944027 (2003m:35259)

18.
F.Treves: Introduction to Pseudodifferential and Fourier Integral Operators, Vol. II. Plenum Press (1980). MR 0597145 (82i:58068)

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Additional Information:

Lidia Maniccia
Affiliation: Department of Mathematics, University of Bologna, Piazza di Porta S.Donato 5, 40127 Bologna, Italy
Email: maniccia@dm.unibo.it

Marco Mughetti
Affiliation: Department of Mathematics, University of Bologna, Piazza di Porta S.Donato 5, 40127 Bologna, Italy
Email: mughetti@dm.unibo.it

DOI: 10.1090/S0002-9947-07-04181-5
PII: S 0002-9947(07)04181-5
Received by editor(s): May 24, 2005
Posted: June 22, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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