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
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10.1512/iumj.2006.55.2626
10.1512/iumj.2006.55.2626
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Indiana Univ. Math. J. 55 (2006) 369 - 388
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