The theorem is
Suppose that $(X,\mathcal{M},\mu)$ and $(Y,\mathcal{N},\nu)$ are measure spaces; $p_{0},p_{1},q_{0},q_{1}$ are elements of $[1,\infty]$ such that $p_{0}\leq q_{0},\ p_{1}\leq q_{1}$, and $q_{0}\neq q_{1}$; and$$\dfrac{1}{p}=\dfrac{1-t}{p_{0}}+\dfrac{t}{p_{1}}\ \text{and}\ \dfrac{1}{q}=\dfrac{1-t}{q_{0}}+\dfrac{t}{q_{1}},\quad \text{where}\ 0<t<1.$$If $T$ is a sublinear map from $L^{p_{0}}(\mu)+L^{p_{1}}(\mu)$ to the space of measurable functions on $Y$ that is weak types $(p_{0},q_{0})$ and $(p_{1},q_{1})$, then $T$ is strong type $(p,q)$. More precisely, if $[Tf]_{q_{j}}\leq C_{j}\lVert f\rVert_{p_{j}}$ for $j=0,1$, then $\lVert Tf\rVert_{q}\leq B_{p}\lVert f\rVert_{p}$ where $B_{p}$ depends only on $p_{j},q_{j},C_{j}$ in addition to $p$; and for $j=0,1,\ B_{p}\lvert p-p_{j}\rvert$ (resp. $B_{p}$) remains bounded as $p\rightarrow p_{j}$ if $p_{j}<\infty$ (resp. $p_{j}=\infty$).
Assuming $q_{j}<\infty$ and $p_{0}<p_{1}<\infty$, the book gives the fomula of $B_{p}$:$$B_{p}=2q^{\frac{1}{q}}\left[ \sum_{j=0}^{1}C_{j}^{q_{j}}\left( \dfrac{p_{j}}{p}\right) ^{\frac{q_{j}}{p_{j}}}\dfrac{1}{\lvert q-q_{j}\rvert}\right] ^{\frac{1}{q}}.$$But leaves the properties of $B_{p}$ out, and that's what I confused. I can't figure out how $p$ approachs to $p_{j}$ and why $B_{p}\lvert p-p_{j}\rvert$ can be unbounded either. Any suggestion would be appreciated.