Аннотация
Using a new approach for the Calderón–Lozanovskii construction $$\varphi (X, L^{\infty})$$ involving an arbitrary ideal space $$X$$ , a Lebesgue space $$L^{\infty}$$ , and a concave function $$\varphi$$ , an exact description of the multiplier space $$M(\varphi_0 (X, L^{\infty}) \to \varphi_1 (X, L^{\infty}))$$ is given, provided that the ratio $${{\varphi_0(\cdot, 1)} /{\varphi_1(\cdot, 1)}}$$ does not increase. Namely, it is shown that the equality $$M(\varphi_0 (X, L^{\infty}) \to \varphi_1 (X, L^{\infty}))=\varphi_2 (X, L^{\infty})$$ is satisfied, where the function $$\varphi_2 $$ is determined constructively from the functions $$\varphi_0, \varphi_1$$ . The absence of restrictions on the ideal space $$X$$ and the exact description of the function $$\varphi_2 $$ enables us to apply the results thus obtained to a wide class of ideal spaces that are not symmetric and cannot be reduced to symmetric ones by an introduction of weight functions, for example, Morrey spaces.