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# Spaces of Lorentz Multipliers

We study when the spaces of Lorentz multipliers from $L^{p,t} \rightarrow L^{p,s}$ are distinct. Our main interest is the case when $s  Keywords: multipliers, convolution operators, Lorentz spaces, Lorentz-improving multipliers  MSC Classifications: 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 42A45 - Multipliers 46E30 - Spaces of measurable functions ($L^p\$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)