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A Failure of Stability Under Complex Interpolation

Published online by Cambridge University Press:  20 November 2018

William C. Connett  and
Alan L. Schwartz
William C. Connett
Affiliation:
University of Missouri-St. Louis, St. Louis, Missouri
Alan L. Schwartz
Affiliation:
University of Missouri-St. Louis, St. Louis, Missouri
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Let denote the spaces of Bessel potentials as denned and discussed in [6]. When 1 < q < ∞ and α is an integer , the Sobolev space which consists of functions Fin Lq with α derivatives in Lq and with norm

If now we make the change of variables x = ev, f(x) = F (In x) it is easily seen that the ratio

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1167 - 1170
Copyright
Copyright © Canadian Mathematical Society 1977

References

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