Square function estimates and the Kato problem for second order parabolic operators in Rn+1Rn+1

In [4] the Kato square root problem for second order complex uniformly elliptic operators of the form L=−div(A∇f)L=−div(A∇f), with only bounded and measurable coefficients, was solved. The solution is a consequence of a square function estimate for the operator (1+λ2L)−1λL(1+λ2L)−1λL. This and related square function estimates have recently spurred a wave of new and ground breaking results in the area of elliptic PDEs. In this paper we establish similar square function estimates for second order parabolic operators in Rn+1Rn+1 of the form ∂t+L∂t+L paving the way for important developments in the area of parabolic PDEs.