Abstract
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.
