Suppose \(z_0\in \mathbb{R}\), \(f(z)\) is holomorphic on \(D(z_0,5r)\), \(I\subseteq \mathbb{R}\) is a bounded, \(z_0\in I\), \(S\subseteq I\) is a measurable subset with nonzero measure and \(p\ge 1\). If \(\lvert f(z_0)\rvert\ge 1\) and \(M=\max_{|z-z_0|\le 4r} |f(z)|\), then
\begin{equation*} \lVert f\rVert_{L^p(I)} \le \biggl(\frac{24\lvert I\rvert}{|S|}\biggr)^{2 \frac{\log M}{\log 2} + \frac{1}{p}} \lVert f\rVert_{L^p(S)}. \end{equation*}