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A Proof of the Calderon Extension Theorem

Published online by Cambridge University Press:  20 November 2018

J. Marsden
J. Marsden*
Affiliation:
University of Toronto, Toronto Ontario
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In this note we outline a proof of the Calderon extension theorem by a technique similar to that for the Whitney extension theorem. For classical proofs, see Calderon [2] and Morrey [4]. See also Palais [6, p. 170]. Our purpose is thus to give a more unified proof of the theorem in the various cases. In addition, the proof applies to the Holder spaces Ck+α, which was used in [3], and applies to regions satisfying the "cone condition" of Calderon.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 133 - 136
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Abraham, R., and Robbin, J., Transversal mappings and flows, Benjamin, New York, 1968.Google Scholar
2. Calderon, A.P., Lebesgue spaces of differentiate functions and distributions, Symposia in Pure Mathematics, Vol. 4, Amer. Math. Soc, Providence, R.I., 1961.Google Scholar
3. Ebin, D., and Marsden, J., Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102–163.Google Scholar
4. Morrey, C.B., Multiple integrals in the calculus of variations, Springer Verlag, New York, 1966.Google Scholar
5. Palais, R.S., Foundations of global nonlinear analysis, Benjamin, New York, 1968.Google Scholar
6. Palais, R.S., Seminar on Atiyah Singer index theorem, Princeton Univ. Press, 1965.Google Scholar