Principal parts of operators in the $\bar{\partial}$-Neumann problem on strictly pseudoconvex non-smooth domains Dariush EhsaniIngo Lieb 32A2532W05dbar Neumann problemintegral representationsnon-smooth domains Working on Henkin-Leiterer domains, we describe the integral kernels of operators $N_q$, $\bar{\partial}N_q$, and $\bar{\partial}^{\ast}N_q$, which arise in the $\bar{\partial}$-Neumann problem. Explicit integral kernels which account for the main mapping properties of the operators are constructed, and weighted $L^p$ estimates are given. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4606 10.1512/iumj.2012.61.4606 en Indiana Univ. Math. J. 61 (2012) 795 - 830 state-of-the-art mathematics http://iumj.org/access/