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February 1994 Lorentz spaces as $L_1$-modules and multipliers
Sadahiro SAEKI, Edward L. THOME
Hokkaido Math. J. 23(1): 55-92 (February 1994). DOI: 10.14492/hokmj/1381412486


Let $w$ be a weight function on a locally compact group $G$, so that the weighted $L_{1}$-space $L_{1}(w)$ forms a Banach algebra under convolution. Suppose that $G$ acts on a locally compact space $\Omega$, and that $B$ is a Banach space consisting of Radon measures on $\Omega$ which is also a left Banach $L_{1}(w)$-module. Under certain conditions on $B$, we shall characterize those bounded linear operators $T:L_{1}(w)\arrow B$ which satisfy $T(f*g)=f*T(g)$. We shall also show that there are numerous examples of Lorentz spaces which form left Banach $L_{1}(w)$-modules with respect to appropriate weight functions.


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Sadahiro SAEKI. Edward L. THOME. "Lorentz spaces as $L_1$-modules and multipliers." Hokkaido Math. J. 23 (1) 55 - 92, February 1994.


Published: February 1994
First available in Project Euclid: 10 October 2013

zbMATH: 0799.46031
MathSciNet: MR1263824
Digital Object Identifier: 10.14492/hokmj/1381412486

Rights: Copyright © 1994 Hokkaido University, Department of Mathematics


Vol.23 • No. 1 • February 1994
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