Geodesic
Additive Functionals on Lorentz Spaces
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 31-37

Voir la notice de l'article provenant de la source Cambridge University Press

If (X, β, μ) is a σ-finite, non-atomic measure space, and φ is an increasing non-negative concave function defined on the positive real numbers, we give a set of necessary and sufficient conditions for an additive functional T on the Lorentz space Nφ to have an integral representation with a Caratheodory kernel. In the special case when T is statistical we classify the functional properties (enjoyed by the kernels) in terms of the Lorentz norm on the space.
DOI : 10.4153/CMB-1984-004-3
Mots-clés : 46E30, 47H99 
Ghatage, Pratibha G. Additive Functionals on Lorentz Spaces. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 31-37. doi: 10.4153/CMB-1984-004-3
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[1] 1. Batt, L. and Gruber, M., Additive operators on Lϕ and their Caratheodory kernels, Comment. Math. Special issue 2 (1979), 1-15. Google Scholar

[2] 2. Dunford, N. and Schwartz, J. T., Linear Operators I, General Theory, Pure and Applied Math., Vol. 7, Interscience, New York, 1958. Google Scholar

[3] 3. Mizel, V. J., Characterization of non-linear transformations possessing kernels, Can. J. Math., Vol. 22, No. 3, 1970, 449-471. Google Scholar

[4] 4. Mizel, V. J. and Sundaresan, K., Representation of vector-valued non-linear functions, Trans. AMS, Vol. 159, 1971, 11-127. Google Scholar

[5] 5. Steigerwalt, M. S. and White, A. J., Some function spaces related to Lp spaces, Proc. London Math. Soc. (3) Vol. 22, 1971, 137-163. Google Scholar

[6] 6. Sundaresan, K., Additive junctionals on Orlicz spaces, Studia Math., Vol. 32, 1969, 269-276. Google Scholar

[7] 7. Frewnowski, L. and Orlicz, W., Continuity and representation of orthogonally additive junctionals, Bull. Acad. Polon. Sci. Deri. Sci-Math-Astronom-Phys. 17 (1969), 647-653. Google Scholar

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