On interpolation of operator, which is the sum of weighted Hardy-Littlewood and Cesaro mean operators

It is proved that operators, which are the sum of weighted Hardy-Littlewood $\int\limits_0^1 f(xt) \psi(t) dt$ and Cesaro $\int\limits_0^1 f(\frac{x}{t}) t^{-n} \psi(t) dt$ mean operators, are limited on Lorentz spaces $\Lambda_{\varphi, a} (\mathbb{R})$, if the functions $f(x) \in \Lambda_{\varphi, a}(\mathbb{R})$ satisfy the condition $|f(-x)| = |f(x)|$, $x > 0$, for such non-increasing semi-multiplicative functions $\psi$, for which the next conditions are satisfied: $\frac{M_1}{\psi(t)} \leqslant \psi(\frac{1}{t}) \leqslant \frac{M_2}{\psi(t)}$, for all $0 0$.