Journal of Mathematics of Kyoto University

On the inclusion of some Lorentz spaces

A. Turan Gürkanli

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Abstract

Let $(X,\Sigma ,\mu )$ be a measure space. It is well known that $l^{p}(X) \subseteq l^{q}(X)$ whenever $0 < p \leq q \leq \infty$. Subramanian [12] characterized all positive measures $\mu$ on $(X,\Sigma )$ for which $L^{p}(\mu ) \subseteq L^{q}(\mu )$ whenever $0 < p \leq q \leq \infty$ and Romero [10] completed and improved some results of Subramanian [12]. Miamee [6] considered the more general inclusion $L^{p}(\mu ) \subseteq L^{q}(\nu )$ where $\mu$ and $\nu$ are two measures on $(X,\Sigma )$.

Let $L(p_{1}, q_{1})(X,\mu )$ and $L(p_{2},q_{2})(X,\nu )$ be two Lorentz spaces,where $0 < p_{1}, p_{2} < \infty$ and $0 < q_{1}, q_{2} \leq \infty$. In this work we generalized these results to the Lorentz spaces and investigated that under what conditions $L(p_{1}, q_{1})(X,\mu ) \subseteq L(p_{2},q_{2})(X,\nu )$ for two different measures $\mu$ and $\nu$ on $(X,\Sigma )$.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 2 (2004), 441-450.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283559

Digital Object Identifier
doi:10.1215/kjm/1250283559

Mathematical Reviews number (MathSciNet)
MR2081078

Zentralblatt MATH identifier
1090.46023

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citation

Gürkanli, A. Turan. On the inclusion of some Lorentz spaces. J. Math. Kyoto Univ. 44 (2004), no. 2, 441--450. doi:10.1215/kjm/1250283559. https://projecteuclid.org/euclid.kjm/1250283559


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