# Comparison of Orlicz-Lorentz spaces

Studia Mathematica (1992)

- Volume: 103, Issue: 2, page 161-189
- ISSN: 0039-3223

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topMontgomery-Smith, S.. "Comparison of Orlicz-Lorentz spaces." Studia Mathematica 103.2 (1992): 161-189. <http://eudml.org/doc/215943>.

@article{Montgomery1992,

abstract = {Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Mastyło, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space, extending results of Lorentz and Raynaud. We also give an example of a rearrangement invariant space that is not an Orlicz-Lorentz space.},

author = {Montgomery-Smith, S.},

journal = {Studia Mathematica},

keywords = {Orlicz-Lorentz spaces; comparing the Orlicz-Lorentz norms; Lorentz- Sharpley space; rearrangement invariant space},

language = {eng},

number = {2},

pages = {161-189},

title = {Comparison of Orlicz-Lorentz spaces},

url = {http://eudml.org/doc/215943},

volume = {103},

year = {1992},

}

TY - JOUR

AU - Montgomery-Smith, S.

TI - Comparison of Orlicz-Lorentz spaces

JO - Studia Mathematica

PY - 1992

VL - 103

IS - 2

SP - 161

EP - 189

AB - Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Mastyło, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space, extending results of Lorentz and Raynaud. We also give an example of a rearrangement invariant space that is not an Orlicz-Lorentz space.

LA - eng

KW - Orlicz-Lorentz spaces; comparing the Orlicz-Lorentz norms; Lorentz- Sharpley space; rearrangement invariant space

UR - http://eudml.org/doc/215943

ER -

## References

top- [B-R] C. Bennett and K. Rudnick, On Lorentz-Zygmund spaces, Dissertationes Math. 175 (1980). Zbl0456.46028
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- [Ka1] A. Kamińska, Some remarks on Orlicz-Lorentz spaces, Math. Nachr., to appear.
- [Ka2] A. Kamińska, Extreme points in Orlicz-Lorentz spaces, Arch. Math. (Basel), to appear.
- [Ka3] A. Kamińska, Uniform convexity of generalized Lorentz spaces, ibid., to appear.
- [K-R] M. A. Krasnosel'skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Noordhoff, 1961.
- [Lo1] G. G. Lorentz, Some new function spaces, Ann. of Math. 51 (1950), 37-55.
- [Lo2] G. G. Lorentz, On the theory of spaces Λ, Pacific J. Math. 1 (1951), 411-429.
- [Lo3] G. G. Lorentz, Relations between function spaces, Proc. Amer. Math. Soc. 12 (1961), 127-132.
- [Lu] W. A. J. Luxemburg, Banach Function Spaces, Thesis, Delft Technical Univ., 1955.
- [Ma] L. Maligranda, Indices and interpolation, Dissertationes Math. 234 (1984).
- [My] M. Mastyło, Interpolation of linear operators in Calderón-Lozanovskii spaces, Comment. Math. 26 (2) (1986), 247-256. Zbl0636.46064
- [Mo1] S. J. Montgomery-Smith, The Cotype of Operators from C(K), Ph.D. thesis, Cambridge, 1988.
- [Mo2] S. J. Montgomery-Smith, Boyd indices of Orlicz-Lorentz spaces, in preparation. Zbl0838.46024
- [O] W. Orlicz, Über eine gewisse Klasse von Räumen vom Typus B, Bull. Intern. Acad. Pol. 8 (1932), 207-220. Zbl0006.31503
- [R] Y. Raynaud, On Lorentz-Sharpley spaces, in: Proc. of the Workshop "Interpolation Spaces and Related Topics", Haifa, June 1990, Amer. Math. Soc., to appear.
- [S] R. Sharpley, Spaces ${\Lambda}_{\alpha}\left(X\right)$ and interpolation, J. Funct. Anal. 11 (1972), 479-513. Zbl0245.46043
- [T] A. Torchinsky, Interpolation of operations and Orlicz classes, Studia Math. 59 (1976), 177-207. Zbl0348.46027

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