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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the Sobolev class of a composite function

Authors: Dennis D. Cox and Finbarr O’Sullivan
Journal: Proc. Amer. Math. Soc. 122 (1994), 727-732
MSC: Primary 46E35; Secondary 46E40, 47H30
MathSciNet review: 1203980
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Abstract: It is shown that the Sobolev class of a function of the form $ H(x,\theta (x))$ is the same as the Sobolev class of $ \theta $, for sufficiently smooth H. This result has applications in a perturbation analysis of a nonlinear system of differential equations considered elsewhere.

References [Enhancements On Off] (What's this?)

  • [1] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957 (56 #9247)
  • [2] D. D. Cox and F. O'Sullivan, Penalized likelihood-type estimators for generalized nonparametric regression, Technical Report, Department of Statistics, University of Washington, 1993; J. Multivar. Anal., submitted.
  • [3] Hans Triebel, Interpolation theory, function spaces, differential operators, North-Holland Mathematical Library, vol. 18, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503903 (80i:46032b)

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Additional Information

PII: S 0002-9939(1994)1203980-7
Keywords: Sobolev norm, composite function
Article copyright: © Copyright 1994 American Mathematical Society