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(p, r)-convex functions on vector lattices

Published online by Cambridge University Press:  20 January 2009

Jerzy Szulga
Jerzy Szulga
Affiliation:
Department of MathematicsAuburn UniversityAuburn, AL 36849–5310, U.S.A.
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Abstract

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We study certain convexity-type properties of homogeneous functions on topological vector lattices, focusing on a concept of 0+-convexity, and using some probabilistic inequalities.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 207 - 226
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Aoki, T., Locally bounded linear topological spaces, Proc. Imp. Acad. Tokyo 18 (1942), No. 10.Google Scholar
2.Billingsley, P., Convergence of Probability Measures (Wiley, New York, 1968).Google Scholar
3.Feller, W., An Introduction to Probability Theory and its Applications, 2nd ed. (Wiley, New York, 1971).Google Scholar
4.Kalton, N., Peck, N. and Roberts, J., An F-space Sampler (Cambridge University Press, London Math. Soc. Lecture Notes Series 89, Cambridge, 1984).CrossRefGoogle Scholar
5.Kalton, N., Peck, N. and Roberts, W., L o-valued measures are bounded, Proc. Amer. Math. Soc. 85 (1982), 575–582.Google Scholar
6.Krivine, J., Theoremes de factorisation dans les espaces reticules (vol. 1973–74 of Seminaire Maurey–Schwartz. École Polytechnique, Paris, 1973–1974), pp. Exposes 22–23.Google Scholar
7.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II. Function Spaces (Springer Verlag, Berlin–Heidelberg–New York, 1979).CrossRefGoogle Scholar
8.Luxemburg, W. and Zaanen, A., Reisz Spaces (North-Holland, Amsterdam, 1971).Google Scholar
9.Maurey, A. and Pisier, G., Séries de variables aleatoires vectorielles independantes et propriétés geometriques des espaces de Banach, Studia Math. 58 (1976), 45–90.CrossRefGoogle Scholar
10.Maurey, B., Type et cotype dans les espaces munis de structures locales inconditionneles (vol. 1973–74 of Seminaire Maurey–Schwartz. École Polytechnique, Paris, 1973–1974, pp. Exposes 24–25.Google Scholar
11.Rolewicz, S., On a certain class of linear metric spaces, Bull. Polish Acad. Sci. 5 (1957), 471–473.Google Scholar
12.Rolewicz, S., Metric Linear Spaces (D. Reidel & Polish Sci. Publ., Dordrecht–Boston–Lancaster & Warszawa, 1985).Google Scholar
13.Schaeffer, H., Banach lattices and positive operators (Springer Verlag, Berlin–Heidelberg–New York, 1974).CrossRefGoogle Scholar
14.Szulga, J., A note on hypercontractivity of α-stable random variables, Ann. Probab. 18 (1990), 1746–1758.CrossRefGoogle Scholar