Kato's inequality
Remarks
### Remarks

* Sometimes the inequality is stated in the form

\\Delta f^\+ \\geq \\operatorname{Re}\\left(1\_{\[f\\geq 0]} \\Delta f\\right)\\quad in \\;\\mathcal{D}'(\\Omega)
 where f^\+\=\\operatorname{max}(f,0\) and 1\_{\[f\\geq 0]} is the indicator function.
* If f is continuous in \\Omega then

\\Delta \|f\| \\geq \\operatorname{Re}\\left((\\operatorname{sgn}\\overline f) \\Delta f\\right)\\quad in \\;\\mathcal{D}'(\\{f\\neq 0\\}).

What is the inequality stated in terms of?