摘要：

In this talk, we revisit the weighted L²-theory for the Dirac operator established by Professor Ji Qingchun and Zhu Ke. We then demonstrate that the classicalL²-existence theorem—valid for domains in R²under a subharmonic weight condition—fails in higher dimensions. Finally, we present an improvement upon the results of Ji and Zhu by deriving a refined a priori estimate, thereby overcoming the restrictive structural conditions previously imposed on the weight function.