The $\bar \partial $-problem on q-pseudoconvex domains with applications

Abstract

Abstract For a q-pseudoconvex domain Ω in ℂn, 1 ≤ q ≤ n, with Lipschitz boundary, we solve the $\bar \partial $-problem with exact support in Ω. Moreover, we solve the $\bar \partial $-problem with solutions smooth up to the boundary over Ω provided that it has smooth boundary. Applications are given to the solvability of the tangential Cauchy-Riemann equations on the boundary.