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-calculus for hypoelliptic pseudodifferential operators
Author(s):
Olesya
Bilyj;
Elmar
Schrohe;
Jörg
Seiler
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1645-1656.
MSC (2000):
Primary 35S05, 47A60, 46H30
Posted:
January 13, 2010
MathSciNet review:
2587449
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Abstract:
We establish the existence of a bounded -calculus for a large class of hypoelliptic pseudodifferential operators on and closed manifolds.
References:
-
- 1.
- H. Abels, Bounded imaginary powers and
-calculus of the Stokes operator in two-dimensional exterior domains. Math. Z. 251 (2005), 589-605. MR 2190346 (2006h:35198) - 2.
- H. Amann, M. Hieber, G. Simonett, Bounded
-calculus for elliptic operators. Diff. Integral Eq. 7 (1994), 613-653. MR 1270095 (95a:47046) - 3.
- R. Beals, A general calculus of pseudodifferential operators. Duke Math. J. 42 (1975), 1-42. MR 0367730 (51:3972)
- 4.
- R. Beals, Characterization of pseudodifferential operators and applications. Duke Math. J. 44 (1977), 45-57; Correction, ibid. 46 (1979) 215. MR 0435933 (55:8884); MR 0523608 (80b:47062)
- 5.
- J.-M. Bony, Caractérisations des opérateurs pseudo-différentiels. Séminaire sur les Équations aux Dérivées Partielles, 1996-1997, Exp. No. XXIII, École Polytech., Palaiseau, 1997. MR 1482829 (98m:35233)
- 6.
- E. Buzano, F. Nicola, Complex powers of hypoelliptic pseudodifferential operators. J. Funct. Anal. 245 (2007), 353-378. MR 2309832 (2008c:35025)
- 7.
- S. Coriasco, E. Schrohe, J. Seiler, Bounded imaginary powers of differential operators on manifolds with conical singularities, Math. Z. 244 (2003), 235-269. MR 1992538 (2004e:58043)
- 8.
- S. Coriasco, E. Schrohe, J. Seiler, Bounded
-calculus for differential operators on conic manifolds with boundary. Comm. Partial Differential Equations 32 (2007), 229-255. MR 2304149 (2008i:58024) - 9.
- R. Denk, M. Hieber, J. Prüss,
-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Mem. Amer. Math. Soc. 166 (2003), no. 788. MR 2006641 (2004i:35002) - 10.
- R. Denk, G. Dore, M. Hieber, J. Prüss, A. Venni, New thoughts on old results of R.T. Seeley. Math. Ann. 328 (2004), 545-583. MR 2047641 (2005k:35090)
- 11.
- R. Denk, J. Saal, J. Seiler, Bounded
-calculus for pseudo-differential Douglis-Nirenberg systems of mild regularity. Math. Nachr. 282 (2009), 386-407. MR 2503159 - 12.
- G. Dore, A. Venni, On the closedness of the sum of two closed operators. Math. Z. 196 (1987), 189-201. MR 910825 (88m:47072)
- 13.
- X.T. Duong, G. Simonett,
-calculus for elliptic operators with nonsmooth coefficients. Differential Integral Equations 10 (1997), 201-217. MR 1424807 (98a:47052) - 14.
- X.T. Duong,
functional calculus of elliptic operators with coefficients on spaces of smooth domains. J. Austral. Math. Soc. Ser. A 48 (1990), 113-123. MR 1026842 (91c:47104) - 15.
- J. Escher, J. Seiler, Bounded
-calculus for pseudodifferential operators and applications to the Dirichlet-Neumann operator. Trans. Amer. Math. Soc. 360 (2008), 3945-3973. MR 2395160 (2009j:47096) - 16.
- B. Gramsch, Relative Inversion in der Störungstheorie von Operatoren und
-Algebren. Math. Ann. 269 (1984), 27-71. MR 756775 (86j:47065) - 17.
- L. Hörmander, The Weyl calculus of pseudodifferential operators. Comm. Pure Appl. Math., 32 (1979), 360-444. MR 0517939 (80j:47060)
- 18.
- H. Kumano-go,
Pseudodifferential operators. The MIT Press, Cambridge, MA, and London, 1981. MR 0666870 (84c:35113) - 19.
- H. Kumano-go, C. Tsutsumi, Complex powers of hypoelliptic pseudo-differential operators and applications. Osaka J. Math. 10 (1973), 147-174. MR 0328392 (48:6734)
- 20.
- P.C. Kunstmann, L. Weis, Maximal
-regularity for parabolic equations, Fourier multiplier theorems and -functional calculus. In Functional Analytic Methods for Evolution Equations, Lecture Notes in Math., 1855, Springer, Berlin, 2004. MR 2108959 (2005m:47088) - 21.
- A. McIntosh, Operators which have an
functional calculus. In B. Jeffries et al. (eds.), Miniconference on Operator Theory and Partial Differential Equations, Proc. Centre Math. Anal. Austral. Nat. Univ., 14, Austral. Nat. Univ., Canberra, 1986. MR 0912940 (88k:47019) - 22.
- E. Schrohe, A
algebra of pseudodifferential operators on noncompact manifolds. Arch. Math. (Basel) 51 (1988), 81-86. MR 954072 (89i:47092) - 23.
- R. Seeley, Complex powers of an elliptic operator. In Amer. Math. Soc. Proc. Symp. Pure Math., 10, Amer. Math. Soc., Providence, RI, 288-307, 1967. MR 0237943 (38:6220)
- 24.
- R. Seeley, Norms and domains of the complex powers
. Amer. J. Math. 93 (1971), 299-309. MR 0287376 (44:4582) - 25.
- J. Ueberberg, Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der
-Theorie, Manuscripta Math. 61 (1988), 459-475. MR 952090 (89g:47070) - 26.
- L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math., 230, Springer, Berlin-Heidelberg-New York, 1971. MR 0467234 (57:7098)
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Additional Information:
Olesya
Bilyj
Affiliation:
Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email:
Olesya_Bilyj@web.de
Elmar
Schrohe
Affiliation:
Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email:
schrohe@math.uni-hannover.de
Jörg
Seiler
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, United Kingdom
Email:
j.seiler@lboro.ac.uk
DOI:
10.1090/S0002-9939-10-10271-8
PII:
S 0002-9939(10)10271-8
Received by editor(s):
February 16, 2009
Posted:
January 13, 2010
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2010,
By the authors
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