During my graduate studies I've been told that pseudo-differential operators with symbols in $S^0=S^0_{1,0}$ (the simplest class) are bounded $L^2 \to L^2$, and also $L^p \to L^p$ for all $p \in (1, \infty)$. I have also heard that such pseudo-differential operators need not be bounded $L^{\infty} \to L^{\infty}$. But no counter examples were presented to me and I can't find any counter example in any book I came across. The Hilbert transform (in Fourier space $\widehat{Hf}(\xi)=i\operatorname{sgn}(\xi) \;\hat f (\xi)$) is unbounded $L^{\infty} \to L^{\infty}$ but strictly speaking it is not a standard pseudo-differential operator.
What are the canonical examples of zeroth order pseudo-differential operators that are not bounded $L^{\infty} \to L^{\infty}$?
If there is a "standard" reference dealing with this problem I would be glad to know where to read it, but any relevant reference would be great!
