Abstract
We prove new bilinear estimates for the
$X^{s,b}_{\pm}({\mathbb R}^2)$
spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on ℝ1+1. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka and Tao, we extend the work of Tesfahun on global existence below the charge class for the Dirac–Klein–Gordon equation on ℝ1+1.