The solution of the Kato square root problem for second order elliptic operators on Rn

By P. Auscher, S. Hofmann, Michael T. Lacey, A. Mcintosh, P. Tchamitchian. 2002

389 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/22fd4fb966a9504e25babae2ecd47a186a884911

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In Applied Mathematics

1. P. Auscher
2. S. Hofmann
3. J. M. Martell
4. Tuomas Hytönen
5. Xuan Thinh Duong
6. A. Mcintosh
7. Dachun Yang
8. J. V. Neerven

In Mathematical Physics

1. P. Auscher
2. S. Hofmann
3. J. M. Martell
4. J. V. Neerven
5. A. Axelsson
6. Tuomas Hytönen
7. A. Mcintosh
8. Mark Veraar

Citations in the corpus

• Solvability of elliptic systems with square integrable boundary data (2008, background): “This is a non-trivial result and is in fact equivalent to the Kato square root problem, proved by Auscher, Hofmann, Lacey, McIntosh and Tchamitchian [5].”
• Quadratic estimates and functional calculi of perturbed Dirac operators (2004, neutral): “This result was proved in a series of papers by Hofmann– McIntosh [18], Auscher–Hofmann–Lewis–Tchamitchian [3], Hofmann– Lacey–McIntosh [17], and, in full generality, by Auscher–Hofmann–Lacey–”
• Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I (2009, methodology): “1] elaborating on the technology for the solution of the Kato problem by Auscher, Hofmann, Lacey, McIntosh and Tchamitchian [10]; a more direct proof is proposed in Auscher, Axelsson and McIntosh [8].”
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, background): “In fact, this criterion is in the air in [Fef] but, still, [BK1] brings some novelty such as the removal of the mean value property already observed in [DMc] when p = 1. See also [BK2] and [HM] for Lp bounds p AHLMcT ].”
• Weak type (p,p) estimates for Riesz transforms (2004, background): “For (1) one needed the additional assumption that the estimate already holds for p = 2 which is the so-called Kato conjecture and has recently been solved affirmatively for second and higher order operators L [ AHLMT ] [AHMT].”
• Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients (2007, background): “(n = 2), [AHLT] (when B is a perturbation of a real, symmetric matrix), [HLMc] (when the kernel of the heat semi-group e−tJ has a Gaussian upper bound) and [ AHLMcT ] in general6.”
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators (2006, methodology): “The solution of the Kato conjecture [ AHLMcT ] implies that this operator extends boundedly to L2 (we ignore the Cn-valued aspect of things).”
• Riesz transform on manifolds and heat kernel regularity (2004, methodology): “n particular, the method applies equally well to accretive (i.e. elliptic) divergence form operators on Rn, in which case the L2 bound is equivalent to the solution of the square root problem of Kato [3]. One of the present authors (Auscher) will present the details of this case (as well as related ”