## Journal of Mathematics of Kyoto University

### On the inclusion of some Lorentz spaces

A. Turan Gürkanli

#### 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

https://projecteuclid.org/euclid.kjm/1250283559

Digital Object Identifier
doi:10.1215/kjm/1250283559

Mathematical Reviews number (MathSciNet)
MR2081078

Zentralblatt MATH identifier
1090.46023

#### 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