A priori estimates for second order operators with symplectic characteristic manifold
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- by Lidia Maniccia and Marco Mughetti PDF
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Abstract:
We prove Fefferman’s SAK Principle for a class of classical pseudodifferential operators on $\mathbb {R}^n$ with symplectic characteristic manifold.References
- Richard Beals and Charles Fefferman, On local solvability of linear partial differential equations, Ann. of Math. (2) 97 (1973), 482–498. MR 352746, DOI 10.2307/1970832
- Louis Boutet de Monvel, Alain Grigis, and Bernard Helffer, Parametrixes d’opérateurs pseudo-différentiels à caractéristiques multiples, Journées: Équations aux Dérivées Partielles de Rennes (1975), Astérisque, No. 34-35, Soc. Math. France, Paris, 1976, pp. 93–121 (French). MR 0493005
- C. Fefferman and D. H. Phong, On positivity of pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4673–4674. MR 507931, DOI 10.1073/pnas.75.10.4673
- Charles L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 2, 129–206. MR 707957, DOI 10.1090/S0273-0979-1983-15154-6
- Daisuke Fujiwara, A construction of approximate positive parts of essentially selfadjoint pseudodifferential operators, Comm. Pure Appl. Math. 37 (1984), no. 1, 101–147. MR 728268, DOI 10.1002/cpa.3160370107
- Frédéric Hérau, Fefferman’s SAK principle in one dimension, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 4, 1229–1264 (English, with English and French summaries). MR 1799744
- Lars Hörmander, The Cauchy problem for differential equations with double characteristics, J. Analyse Math. 32 (1977), 118–196. MR 492751, DOI 10.1007/BF02803578
- Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
- Richard Lascar, Propagation des singularités et hypoellipticité pour des opérateurs pseudo-différentiels à caractéristiques doubles, Comm. Partial Differential Equations 3 (1978), no. 3, 201–247 (French). MR 492798, DOI 10.1080/03605307808820064
- N. Lerner and J. Nourrigat, Lower bounds for pseudo-differential operators, Ann. Inst. Fourier (Grenoble) 40 (1990), no. 3, 657–682 (English, with French summary). MR 1091836
- Lidia Maniccia and Marco Mughetti, SAK principle for a class of Grushin-type operators, Rev. Mat. Iberoam. 22 (2006), no. 1, 259–286. MR 2268119, DOI 10.4171/RMI/455
- Lidia Maniccia and Marco Mughetti, Fefferman’s SAK principle and a priori estimates for second order operators, Ann. Univ. Ferrara Sez. VII Sci. Mat. 52 (2006), no. 2, 337–352. MR 2273103, DOI 10.1007/s11565-006-0025-2
- Sami Mustapha, Sous ellipticité dans le cadre du calcul $S(m,g)$, Comm. Partial Differential Equations 19 (1994), no. 1-2, 245–275 (French). MR 1257005, DOI 10.1080/03605309408821016
- Sami Mustapha, Sous-ellipticité dans le cadre du calcul $S(m,g)$. II, Comm. Partial Differential Equations 20 (1995), no. 3-4, 541–566 (French). MR 1318080, DOI 10.1080/03605309508821104
- Alberto Parmeggiani, A class of counterexamples to the Fefferman-Phong inequality for systems, Comm. Partial Differential Equations 29 (2004), no. 9-10, 1281–1303. MR 2103837, DOI 10.1081/PDE-200037706
- Alberto Parmeggiani, Subunit balls for symbols of pseudodifferential operators, Adv. Math. 131 (1997), no. 2, 357–452. MR 1483973, DOI 10.1006/aima.1997.1672
- Daniel Tataru, On the Fefferman-Phong inequality and related problems, Comm. Partial Differential Equations 27 (2002), no. 11-12, 2101–2138. MR 1944027, DOI 10.1081/PDE-120016155
- François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 2, University Series in Mathematics, Plenum Press, New York-London, 1980. Fourier integral operators. MR 597145
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
- Received by editor(s): May 24, 2005
- Published electronically: June 22, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 5193-5206
- MSC (2000): Primary 35B45; Secondary 35S05
- DOI: https://doi.org/10.1090/S0002-9947-07-04181-5
- MathSciNet review: 2327027