Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-12-04T09:50:08.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Real Interpolation of Sobolev Spaces on Subdomains of Rn

Published online by Cambridge University Press:  20 November 2018

R. A. Adams  and
J. J. F. Fournier
R. A. Adams
Affiliation:
University of British Columbia, Vancouver, British Columbia
J. J. F. Fournier
Affiliation:
University of British Columbia, Vancouver, British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The real interpolation method is a very convenient tool in the study of imbedding relationships among Sobolev spaces and some of their fractional order generalizations, (Besov spaces, Nikolskii spaces etc.) Central to the application of these methods is the a priori determination that a given Sobolev space Wk'p(Ω) belongs to an appropriate class of spaces intermediate between two other “extreme” spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 190 - 214
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Adams, R. A., Sobolev spaces (Acedemic Press, New York, 1975).Google Scholar
2. Adams, R. A. and Fournier, J. J. F., Cone conditions and properties of Sobolev spaces, J. Math. Anal. Appl. 61 (1977) (to appear).Google Scholar
3. Besov, O. V., Ilin, V. P. and Nikolskii, S. M., Integral representation of functions and imbedding theorems, (Russian) Nauka, Moscow, 1975.Google Scholar
4. Butzer, P. L. and Berens, H., Semi-groups of operators and approximation (Springer-Verlag, New York, 1967).Google Scholar
5. A. P., Calderôn, Intermediate spaces and interpolation, the complex method, Studia Math. 2J+ 19G4), 113–190.Google Scholar
6. Coifman, R. R. and Weiss, G., Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 2J+2 (Springer-Verlag, Berlin).Google Scholar
7. Coifman, R. R. and Weiss, G., Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645.Google Scholar
8. Fefferman, C., Recent progress in classical Fourier analysis, Proc. of the International Congress of Mathematicians, Vol. I, Vancouver (1974), 95–119.Google Scholar
9. Lions, J. L. and Peetre, J., Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Sci. Publ. Math. 10 (1964), 5–68.Google Scholar
10. Morrey, C. B., Functions of several variables and absolute continuity, II, Duke J. Math. 0 (1940), 197–215.Google Scholar
11. Muramatu, T., On Besov spaces of functions defined in general regions, Publ. RIMS, Kyoto Univ. 6 (1970), 515–543.Google Scholar
12. Muramatu, T., On imbedding theorems for Besov spaces of functions defined in general regions, Publ. RIMS, Kyoto Univ. 7 (1971), 26–285.Google Scholar
13. Muramatu, T., On Besov spaces and Sobolev spaces of generalized functions defined on a general region, Publ. RIMS, Kyoto Univ. 9 (1974), 325–396.Google Scholar
14. Peetre, J., Espaces d'interpolation et théorème de Soboleff, Ann. Inst. Fourier, Grenoble 16 (1966), 279–317.Google Scholar
15. Riviere, N. M. and Sagher, Y., Interpolation betweenL°° and H1, the real method, J. Functional Anal. U (1973), 401–409.Google Scholar
16. Stein, E. M., Singular integrals and differentiability properties of functions (Princeton Univ. Press, Princeton, New Jersey, 1970).Google Scholar
17. Stein, E. M. and Weiss, G., Introduction to Fourier analysis on Euclidean spaces (Princeton Univ. Press, Princeton, New Jersey, 1971).Google Scholar