Impact of Yves Meyer's work on Kato's conjecture

We discuss how the works of Yves Meyer, together with Raphy Coifman, on Calder{ó}n’s program and singular integrals with minimal smoothness in the seventies, paved the way not only to a solution to Kato’s conjecture for square roots of elliptic operators, but also to major developments in elliptic and parabolic boundary value problems with rough coefficients on rough domains.