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Additive Functionals on Lp Spaces

Published online by Cambridge University Press:  20 November 2018

N. Friedman  and
M. Katz
N. Friedman
Affiliation:
University of New Mexico
M. Katz
Affiliation:
University of New Mexico
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In (1) a representation theorem was proved for a class of additive functionals defined on the continuous real-valued functions with domain S = [0, 1]. The theorem was extended to the case where S is an arbitrary compact metric space in (3). Our present purpose is to consider the corresponding class of additive functionals defined on Lp spaces, p > 0. In (4) Martin and Mizel have considered functionals defined on the class of bounded measurable functions which, however, satisfy a certain “stochastic” condition which we do not require.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1264 - 1271
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Chacon, R. V. and Friedman, N., Additive Junctionals, Arch. Rational Mech. Anal., 18 (1965), 230–240.Google Scholar
2. Day, M. M., The spaces Lp with 0 < p < 1, Bull. Amer. Math. Soc., 46 (1940) 816–823.Google Scholar
3. Friedman, N. and Katz, M., A representation theorem for additive Junctionals, Arch. Rational Mech. Anal., 21 (1966), 49–57.Google Scholar
4. Martin, A. D. and Mizel, V. J., A representation theorem for certain nonlinear functionals, Arch. Rational Mech. Anal., 16 (1964), 353–367.Google Scholar