Maximum Principle for estimate norm

Question

I have two functions. A harmonic funcion $u$ in unit ball $B_{1}\subset \mathbb{R}^{n}$ and a function $h$ defined on $B_{1}$ such that $\Delta h=u$ in $B_{1}$ and $h=u$ in $\partial B_{1}$, the author says that : by maximum principle $|| h ||\leq 1$. I do not know how to estimate h, and I do not know what norm it refers to

Answer 1

In this form the statement cannot be correct for any norm.

Let $h$ and $u$ be functions as in the assumptions and let $\lambda \in \mathbb{R}$, then $\lambda h$ and $\lambda u$ satisfy the same assumptions and $\|\lambda h\|$ can be made as large as you want.