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Proceedings of the American Mathematical Society

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The Lorentz space as a dual space

Author: Pratibha G. Ghatage
Journal: Proc. Amer. Math. Soc. 91 (1984), 92-94
MSC: Primary 46E30
MathSciNet review: 735571
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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 ^ * )$.

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  • [2] M. S. Steigerwalt and A. J. White, Some function spaces related to $ {L_p}$ spaces, Proc. London Math. Soc. 22 (1971), 137-163. MR 0279582 (43:5304)
  • [3] W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974. MR 0344043 (49:8783)

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Article copyright: © Copyright 1984 American Mathematical Society

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