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

الأصل · EN

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 Lᵖ, they remain R-bisectorial in Lq for all q close to p. In combination with our earlier results with Portal, which required such R-bisectoriality in different Lq spaces to start with, this shows that the R-bisectoriality in just one Lᵖ actually implies bounded H-infinity calculus in Lq 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.