Title: Singular integrals on product domains

Authors: Hussain Al-Qassem, A. Al-Salman and Y. Pan

Issue: Volume 55 (2006), Issue 1, 369-388

Abstract: 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 $r < 2$.