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Extension operators for Sobolev spaces commuting with a given transform

Published online by Cambridge University Press:  18 May 2009

Viktor Burenkov ,
Bert-Wolfgang Schulze  and
Nikolai N. Tarkhanov
Viktor Burenkov
Affiliation:
University of Wales Cardiff, 23 Senghennydd Road, Cardiff CF2, Wales
Bert-Wolfgang Schulze
Affiliation:
Max-Planck AG “Analysis”, Universität Potsdam, Postfach 60 15 53, 14415 Potsdam, Germany
Nikolai N. Tarkhanov
Affiliation:
Institut Für Mathematik, Universität Potsdam, Postfach 60 15 53, 14415 Potsdam, Germany
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Abstract

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We consider a real-valued function r = M(t) on the real axis, such that M(t) < 0 for t < 0. Under appropriate assumptions on M, the pull-back operator M* gives rise to a transform of Sobolev spaces Ws.p (-∞, 0) that restricts to a transform of Ws.p(-∞, ∞). We construct a bounded linear extension operator Ws.p(-∞, 0) → Ws.p(−∞, ∞), commuting with this transform.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 291 - 296
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

1.Babich, V. M., On the extension of functions, Uspekhi Mat. Nauk. 8(2 (54)) (1953), 11–113.Google Scholar
2.Hestenes, M. R., Extensions of the range of a differentiable function, Duke Math. J. 8 (1941), 183–192.CrossRefGoogle Scholar
3.Nikol'skii, S. M., On the solution of the polyharmonic equation by a variational method, Dokl. Akad. Nauk SSSR 88 (1953), 409–411 (Russian).Google Scholar
4.Nikol'skii, S. M., Approximation of functions of several variables and embedding theorems (Springer-Verlag, 1974).Google Scholar
5.Schulze, B.-W., Boundary value problems and singular pseudo-differential operators (J. Wiley, 1997).Google Scholar
6.Triebel, H., Theory of function spaces (Birkhäuser, 1983).CrossRefGoogle Scholar