The Kato square root problem for higher order elliptic operators and systems on $ \Bbb R^n $

By P. Auscher, S. Hofmann, A. Mcintosh, P. Tchamitchian. 2001

94 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/711175a201dfe1acf672f827e460441a29d879e5

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

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 ].”
Solvability of elliptic systems with square integrable boundary data (2008, methodology): “For general elliptic systems, the Kato problem was solved by Auscher, Hofmann, McIntosh and Tchamitchian [6], a consequence being the well posedness of (Neu-A) and (Reg-A) for elliptic systems with block form coefficients.”
Carleson measures, trees, extrapolation, and T(b) theorems (2001, background): “…plethat there could be two di erent accretive functions b1;b2 such that T(b1);T (b2) 2 B M O ; and m oreover that the pointwise accretivity condition could be relaxed to a condition holding on varioussortsofaverages-see,e.g.,thenotion of\pseudo-accretivity" de ned in Section 6.1 below).”
The Kato Square Root Problem for Mixed Boundary Value Problems (2004, background): “was solved in [2] by P. Auscher, S. Hofmann, M. Lacey, Ph. Tchamitchian and the third author, and for higher order elliptic operators and systems on Rn in [ 3 ] by”
On a quadratic estimate related to the Kato conjecture and boundary value problems (2008, methodology): “The idea which we use of doing the conical decomposition, not in the space of constants, but within the linear space of matrices to which γt(x) belongs, is an important observation, made in [5] for proving the Kato conjecture for higher order operators and systems.”