Singular integrals on product domains Hussain Al-QassemA. Al-SalmanYibiao Pan 42B2042B1542B25singular integralsproduct domainsrough kernels This paper is concerned with singular integral operators on product domains with rough kernels in $L(\log L)^{2}$. We prove, among other things, $L^{p}$ bounds $(1 < p < \infty )$ for such singular integral operators as well as for their corresponding maximal truncated singular integrals. We also establish the optimality of our condition in the sense that the space $L(\log L)^{2}$ cannot be replaced by $L(\log L)^{r}$ for any $r < 2$. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2626 10.1512/iumj.2006.55.2626 en Indiana Univ. Math. J. 55 (2006) 369 - 388 state-of-the-art mathematics http://iumj.org/access/