Mathematical Research Letters

Volume 16 (2009)

Number 5

On Hofmann’s bilinear estimate

Pages: 753 – 760



Pascal Auscher (Université de Paris-Sud)


Using the framework of a previous article joint with Axelsson and McIntosh, we extend to systems two results of S. Hofmann for real symmetric equations and their perturbations going back to a work of B. Dahlberg for Laplace’s equation on Lipschitz domains. The first one is a certain bilinear estimate for a class of weak solutions and the second is a criterion which allows to identify the domain of the generator of the semi-group yielding such solutions.


elliptic systems, Dirichlet problem, quadratic estimates, Carleson measures

2010 Mathematics Subject Classification

35J25, 35J56, 42B25, 47N20

Published 1 January 2009