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H∞ functional calculus of elliptic operators with C∞ coefficients on Lp spaces of smooth domains

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Xuan Thinh Duong
Xuan Thinh Duong
Affiliation:
School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversityNSW, 2109, Australia
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Abstract

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The purpose of this paper is to show that higher order elliptic partial differential operators on smooth domains have an H∞ functional calculus and satisfy quadratic estimates in Lp spaces on these domains.

MSC classification

Secondary: 47A60: Functional calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 113 - 123
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Agmon, S., ‘On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems’, Comm. Pure Appl. Math. 15 (1962), 119–147.CrossRefGoogle Scholar
[2]Cowling, M., McIntosh, A. and Yagi, A., ‘Banach space operators with an H ∞ functional claculs’ (in preparation).Google Scholar
[3]McIntosh, A., ‘Operators which have an H ∞ functional calculus’, Minicoference on Operator Theory and Partial Differential Equations, (Proceedings of the Center for Mathematical Analysis, ANU, Canberra, 14 (1986), 210–231).Google Scholar
[4]Seeley, R., ‘The resolvent of an elliptic boundary problem’, Amer. J. Math. 91 (1969), 889–920.Google Scholar
[5]Seeley, R., ‘Norms and domains of the complete powers AzB’, Amer. J. MAth. 93 (1971), 299–309.CrossRefGoogle Scholar
[6]Seeley, R., Fractional powers of boundary problems, (Proc. Internat. Congr. Math., Nice, 2 (1970), pp. 795–801).Google Scholar
[7]Stein, E., Singular intergrals and differentiability properties of functions, (Princeton Univ. Press, Princeton, N. J., 1970).Google Scholar
[8]Tanabe, H., Equation of evolutions, (Pitman, London, San Francisco and Melbourne, 1979).Google Scholar