Let be a Musielak-Orlicz function satisfying that, for any <!-- MATH $(x,\,t)\in \mathbb{R}^n\times (0,\,\infty )$ --> , <!-- MATH $\varphi (\cdot ,\,t)$ --> belongs to the Muckenhoupt weight class <!-- MATH $A_\infty (\mathbb{R}^n)$ --> with the critical weight exponent <!-- MATH $q(\varphi )\in [1,\,\infty )$ --> and <!-- MATH $\varphi (x,\,\cdot )$ --> is an Orlicz function with <!-- MATH \begin{displaymath} 0