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A New Proof of an Inequality of Heinz

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen
P. S. Bullen*
Affiliation:
University of British Columbia
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In a recent paper, [l], Dixmier has proved Heinz' inequality by deducing it from a lemma due to Thorin. In this note it is proved directly from a convexity theorem.

Let(M(k), ℳ(k), μ(k)), k = 0, …, n, be measure spaces and Lq(k) (M(k), ℳ(k), μ(k)) be all the functions on M(k) such that

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 1 , March 1964 , pp. 97 - 100
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Dixmier, J., Sur une inégalité de E. Heinz. Math. Annalen, 126(1953), 75–78.Google Scholar
2. Stein, E. M. and Weiss, G., Interpolation of Operators with Change of Measures. Trans, of the Amer. Math. Soc., 87(1958), pp. 159–172.Google Scholar