Abstract
For a
q
-pseudoconvex domain Ω in ℂ
n
, 1 ≤
q
≤
n
, with Lipschitz boundary, we solve the
-problem with exact support in Ω. Moreover, we solve the
-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.