  We show that one of the two important uncertainty principles derived by
Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary
maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main
tool is the Clarkson inequalities. We also derive a nonlinear uncertainty
principle for weak parallelogram spaces and Type-p Banach spaces.
