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

• Published in: Advances in mathematics (New York. 1965) Vol. 293; pp. 1 - 36
• Main Author: Nyström, K.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 30.04.2016
• Subjects: Carleson measure; Complex coefficients; Kato problem; Second order parabolic operator; Square function estimate; Square root; Carleson measure; Square root; Kato problem; Square function estimate; Complex coefficients; Second order parabolic operator; 35K10
• ISSN: 0001-8708; 1090-2082; 1090-2082
• DOI: 10.1016/j.aim.2016.02.006

In [4] the Kato square root problem for second order complex uniformly elliptic operators of the form 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. 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+1 of the form ∂t+L paving the way for important developments in the area of parabolic PDEs.