Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Inequalities of Young-type

  • 56 Accesses

  • 4 Citations

Abstract

Necessary and sufficient conditions are given for the Young-type inequalityxy≤f(x)+g(y) (x, y>0) to hold wheref, g are arbitrary real functions on the positive half line.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Birnbaum, Z., Orlicz, W.: Über eine Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen. Studia Math.3, 1–67 (1931).

  2. [2]

    Boas, R. P., Marcus, M. B.: Inequalities involving a function and its inverse. SIAM J. Math. Anal. Appl.4, 585–591 (1973).

  3. [3]

    Boas, R. P., Marcus, M. B.: Generalizations of Young's inequality. J. Math. Anal. Appl.46, 36–40 (1974).

  4. [4]

    Boas, R. P., Marcus, M. B.: Inverse functions and integration by parts. Amer. Math. Monthly81, 760–761 (1974).

  5. [5]

    Bourbaki, N.: Fonctions d'une Variable Réelle. Paris: Hermann. 1949.

  6. [6]

    Cooper, R.: Notes on certain inequalities I. J. London Math. Soc.2, 17–21 (1927).

  7. [7]

    Cunningham, F., Jr., Grossman, N.: On Young's inequality. Amer. Math. Monthly78, 781–783 (1971).

  8. [8]

    Dankert, G., König, H.: Über die Höldersche Ungleichung in Orlicz-Räumen. Arch. Math.18, 61–75 (1967).

  9. [9]

    Diaz, J. B., Metcalf, F. T.: An analytic proof of Young's inequality. Amer. Math. Monthly77, 603–609 (1970).

  10. [10]

    Klambauer, G.: Integration by parts and inverse functions. Amer. Math. Monthly85, 668–699 (1978).

  11. [11]

    Krasnosel'skii, M. A., Rutickii, Ya. B.: Convex Functions and Orlicz Spaces. Groningen: Noordhoff. 1961.

  12. [12]

    Losonczi, L.: Hölder-type inequalities. General Inequalities 3. In: Proc. 3rd Inter. Conf. Math. Res. Inst., Oberwolfach, pp. 91–106. Basel-Boston: Birkhäuser 1983.

  13. [13]

    Mitrinovic, D. S.: Analytic Inequalities. Berlin-Heidelberg-New York: Springer. 1970.

  14. [14]

    Oppenheim, A.: Note on Mr. Cooper's generalization of Young's inequality. J. London Math. Soc.2, 21–23 (1927).

  15. [15]

    Young, W. H.: On classes of summable functions and their Fourier series. Proc. Royal Soc. LondonA 87, 225–229 (1912).

  16. [16]

    Zaanen, A. C.: Linear Analysis. New York-Amsterdam: Interscience. 1953.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Losonczi, L. Inequalities of Young-type. Monatshefte für Mathematik 97, 125–132 (1984). https://doi.org/10.1007/BF01653242

Download citation

Keywords

  • Real Function
  • Half Line
  • Positive Half Line
  • Positive Half
  • Arbitrary Real Function