Stability in p of the H-infinity calculus of first-order systems in L^p

Abstract

We study certain differential operators of the form AD arising from a first-order approach to the Kato square root problem. We show that if such operators are R-bisectorial in L^p, they remain R-bisectorial in L^q for all q close to p. In combination with our earlier results with Portal, which required such R-bisectoriality in different L^q spaces to start with, this shows that the R-bisectoriality in just one L^p actually implies bounded H-infinity calculus in L^q for all q close to p. We adapt the approach to related second-order results developed by Auscher, Hofmann and Martell, and also employ abstract extrapolation theorems due to Kalton and Mitrea.

13 pages, to appear in Proc. Centre Math. Appl. Austral. Nat. Univ.