Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-07-05T11:03:30.419Z Has data issue: false hasContentIssue false

Variants of the Hölder Inequality and its Inverses

Published online by Cambridge University Press:  20 November 2018

Chung-Lie Wang*
Affiliation:
Dept. of Mathematics, University of Regina, Regina, CanadaS4S 0A2
Rights & Permissions [Opens in a new window]

Abstract

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.

This paper presents variants of the Holder inequality for integrals of functions (as well as for sums of real numbers) and its inverses. In these contexts, all possible transliterations and some extensions to more than two functions are also mentioned.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bartle, R. G., The elements of integration, John-Wiley and Sons, New York, 1966.Google Scholar
2. Beckenbach, E. F. and Bellman, R., Inequalities, Springer-Verlag, Berlin, 1961.Google Scholar
3. Chung, K. L., A course in probability theory. Harcourt, Brace & World, Inc., New York, 1968.Google Scholar
4. Diaz, J. B. and Metcalf, F. T.. Complementary inequalities I: Inequalities complementary to Cauchy's inequality for sums of real numbers, J. Math. Anal, and Appl. 9 (1964), 59-74.Google Scholar
5. Diaz, J. B. and Metcalf, F. T., Complementary inequalities II: Inequalities complementary to the Buniakowsky-Schwarz inequality for integrals, J. Math. Anal, and Appl. 9 (1964), 278-293.Google Scholar
6. Diaz, J. B. and Metcalf, F. T., Stronger forms of a class of inequalities of G. Pόlya-G. Szegö and Kantorovich, Bull. Amer. Math. Soc. 69 (1963), 415-418.Google Scholar
7. Diaz, J. B., Goldman, A. J., and Metcalf, F. T., Equivalence of certain inequalities complementing those of Cauchy-Schwarz and Holder, J. Res. NBS 68B (Math, and Math. Phys.) No. 2 (1964), 147-149.Google Scholar
8. Dunford, N. and Schwartz, J. T., Linear operators Part I: General Theory, Interscience, New York, 1958.Google Scholar
9. Greub, W. and Rheinboldt, W., On a generalization of an inequality of L. V. Kantorovich, Proc. America Math. Soc. 10 (1959), 407-415.Google Scholar
10. Kantorovich, L. V., Functional analysis and applied mathematics, Uspehi Mat. Nauk 3 (1948), 89-185 (also translated from the Russian by C. D. Benster, Nat. Bur. Standards Report No. 1509, 1952).Google Scholar
11. Munroe, M. E., Introduction to measure and integration, Addison-Wesley, Reading, Mass., 1953.Google Scholar
12. Pόlya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Vol. I. Berlin, 1925.Google Scholar
13. Schweitzer, P., Egy egyenlotlenség ax aritmetikai középértékröl (An inequality concerning the arithmetic mean), Math, es phys. lopok 23 (1914), 257-261.Google Scholar
14. Wang, Chung-Lie, An extension of a Bellman inequality, Utilitas mathematica, 8 (1975), 251-256.Google Scholar