Interpolation of operators of weak type $(\varphi,\varphi)$

Considering the measurable and nonnegative functions $\varphi$ on the half-axis $[0,\infty)$ such that $\varphi(0)=0$ and $\varphi(t)\to\infty$ as $t\to\infty$, we study the operators of weak type $(\varphi,\varphi)$ that map the classes of $\varphi$-Lebesgue integrable functions to the space of Lebesgue measurable real functions on $\mathbb R^n$. We prove interpolation theorems for the subadditive operators of weak type $(\varphi_0,\varphi_0)$ bounded in $L_\infty(\mathbb R^n)$ and subadditive operators of weak types $(\varphi_0,\varphi_0)$ and $(\varphi_1,\varphi_1)$ in $L_\varphi(\mathbb R^n)$ under some assumptions on the nonnegative and increasing functions $\varphi(x)$ on $[0,\infty)$. We also obtain some interpolation theorems for the linear operators of weak type $(\varphi_0,\varphi_0)$ bounded from $L_\infty(\mathbb R^n)$ to $BMO(\mathbb R^n)$. For the restrictions of these operators to the set of characteristic functions of Lebesgue measurable sets, we establish some estimates for rearrangements of moduli of their values; deriving a consequence, we obtain a theorem on the boundedness of operators in rearrangement-invariant spaces.