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

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

2010-03-29

arxiv.org/abs/1003.5456v1

Mathematics

Functional Analysis

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

Scientific paper

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.

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