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Rearrangement Inequalities

Published online by Cambridge University Press:  20 November 2018

Peter W. Day*
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania
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In recent years a number of inequalities have appeared which involve rearrangements of vectors in Rn and of measurable functions on a finite measure space. These inequalities are not only interesting in themselves, but also are important in investigations involving rearrangement invariant Banach function spaces and interpolation theorems for these spaces [2; 8; 9].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Apostol, T. M., Mathematical analysis (Addison-Wesley, 1957).Google Scholar
2. Chong, K. M. and Rice, N. M., Equimeasurable rearrangements of functions, Queen's Papers in Pure and Applied Mathematics, No. 28 (Queen's University, Kingston, Ontario, Canada, 1971).Google Scholar
3. Halmos, P. R., Functions of Integrable Functions, J. Indian Math. Soc. 11 (1947), 8184.Google Scholar
4. Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities (Cambridge University Press, Cambridge, 1934).Google Scholar
5. Hewett, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, New York, 1965).Google Scholar
6. David, London, Rearrangement inequalities involving convex functions, Pacific J. Math. 34 (1970), 749752.Google Scholar
7. Lorentz, G. G., An Inequality for rearrangements, Amer. Math. Monthly 60 (1953), 176179.Google Scholar
8. Lorentz, G. G. and Shimogaki, T., Interpolation theorems for operators in function spaces, J. Functional Analysis 2 (1968), 3151.Google Scholar
9. Luxemburg, W. A. J., Rearrangement invariant Banach function spaces, Queen's Papers in Pure and Applied Math. 10 (1967), 83144.Google Scholar
10. Henryk, Mine, Rearrangement theorems, Notices Amer. Math. Soc. 17 (1970), 400.Google Scholar
11. Mitrinovic, D. S., Analytic inequalities (Springer-Verlag, New York, 1970).Google Scholar
12. Ruderman, H. D., Two new inequalities, Amer. Math. Monthly 59 (1952), 2932.Google Scholar