On the Kato problem and extensions for degenerate elliptic operators
On the Kato problem and extensions for degenerate elliptic operators
We study the Kato problem for degenerate divergence form operators. This was begun by Cruz-Uribe and Rios who proved that given an operator $L_w=-w^{-1}{\rm div}(A\nabla)$, where $w\in A_2$ and $A$ is a $w$-degenerate elliptic measure (i.e, $A=w\,B$ with $B$ an $n\times n$ bounded, complex-valued, uniformly elliptic matrix), then $L_w$ satisfies …