The Lorentz space as a dual space
HTML articles powered by AMS MathViewer
- by Pratibha G. Ghatage PDF
- Proc. Amer. Math. Soc. 91 (1984), 92-94 Request permission
Abstract:
If $(X,S,\mu )$ is a finite, completely nonatomic measure space and $\phi (t) = {t^{1/p}}(p > 1)$ then the Lorentz space ${N_\phi }$ is the dual space of the closed span of simple functions in ${M_\phi }( = N_\phi ^ * )$.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- M. S. Steigerwalt and A. J. White, Some function spaces related to $L_{p}$ spaces, Proc. London Math. Soc. (3) 22 (1971), 137–163. MR 279582, DOI 10.1112/plms/s3-22.1.137
- Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. MR 0344043
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 92-94
- MSC: Primary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735571-X
- MathSciNet review: 735571