Abstract
Some important results of the theory of rearrangement invariant spaces can be extended in the framework of the theory of rearrangement invariant p-spaces, where 0<p<1.
A special attention is paid to the primariness of the separable r.i.p-spaces, whose Boyd indices are non-trivial.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Bennet-An extension of Riesz-Thorin theorem. Lecture Notes in Math., vol.604, Springer-Verlag, Berlin and New York, 1977.
R. Hunt-On L(p,q) spaces, L'enseignement mathématique 12, 249–274 (1966).
N.J. Kalton-The endomorphismes of Lp (0⩽p⩽1) Indiana Univ. Math. J. 27, 353–381 (1978).
N.J. Kalton-Linear operators on Lp for 0<p<1. T.A.M.S. 259, 319–355 (1980).
J. Lindenstrauss, L. Tzafriri-Classical Banach spaces I-Springer Verlag, Berlin and New York, 1977.
J. Lindenstrauss, L. Tzafriri-Classical Banach spaces II, Springer Verlag, Berlin and New York, 1979.
G. Lozanovskii-Concerning functions of elements of a vector lattice (russian)-Izv.vishy.ucebn.zav. Mat. 4(431), 45–54, (1973).
N.Popa-Uniqueness of the symmetric structure on Lp(μ) for 0<p<1, Rev. Roum. Math. Pures et Appl. (to appear).
N.Popa-Interpolation theorems for rearrangement invariant p-spaces of functions, for 0<p<1 (to appear).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Popa, N. (1983). The primariness of rearrangement invariant function p-spaces, 0<p⩽1. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061572
Download citation
DOI: https://doi.org/10.1007/BFb0061572
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12298-2
Online ISBN: 978-3-540-39877-6
eBook Packages: Springer Book Archive