On the Sobolev class of a composite function
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- by Dennis D. Cox and Finbarr O’Sullivan PDF
- Proc. Amer. Math. Soc. 122 (1994), 727-732 Request permission
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
- Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957 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.
- H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. MR 500580
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 727-732
- MSC: Primary 46E35; Secondary 46E40, 47H30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1203980-7
- MathSciNet review: 1203980