Maximal accretive operators are infinitesimal generators $T$ of contraction semigroups $S(t)= \exp (-tT),\, t \geq 0.$ In the early sixties Tosio Kato defined the fractional power $T^{\alpha },\, 0 < \alpha <1,$ of an accretive operator $T$ and tried to find its domain. The square root is the most difficult case. Let us assume that $T(f)= -{\rm div}\big (A(x)\nabla f(x)\big )$ where $A(x)= (a_{j, k}(x))_{1\leq j, k \leq n}$ is a uniformly accretive matrix with measurable and bounded entries. P. Auscher et al. succeeded in proving that the domain of $\sqrt T$ is the Sobolev space $H^1(\mathbb {R}^n).$ Here we are entering the new operator theory, beyond pseudodifferential operators, which was foreseen by Alberto Calderón.