In functional analysis, a subfield of mathematics, Kato's inequality is a distributional inequality for the Laplace operator or certain elliptic operators.
It was proven in 1972 by the Japanese mathematician Tosio Kato.
[1] The original inequality is for some degenerate elliptic operators.
[2] This article treats the special (but important) case for the Laplace operator.
is the space of locally integrable functions – i.e., functions that are integrable on every compact subset of their domains of definition.