The general Marcinkiewicz interpolation theorem states as following:
If $T$ is a linear operator of weak type $(p_0,q_0)$ and of weak type $(p_1,q_1)$ where $q_0\neq q_1$, then for each $\theta\in(0,1)$, $T$ is of type $(p,q)$, for $p$ and $q$ with $p\le q$ of the form $$\frac{1}{p} = \frac{1-\theta}{p_0}+\frac{\theta}{p_1},\quad \frac{1}{q} = \frac{1-\theta}{q_0} + \frac{\theta}{q_1}.$$
When we say an operator $T$ is of type $(p,q)$, it means $||Tf||_q \leq C||f||_p$ for some $C$.
When we say an operator $T$ is of weak type $(p,q)$, it means $||Tf||_{q,w} \le C||f||_p$ for some $C$. Here $||·||_{q,w}$ means the best constant $C$ such that $\lambda_f(t)\le \frac{C^q}{t^q}$ holds for all $t$ and $f$, where $\lambda$ is the distribution function.
On wikipedia it says this follows from the former (the restricted from where $p_0=p_1$ and $q_0 = q_1$) through an application of Hölder's inequality and a duality argument. But I do not understand it. Can someone say something more clear?