L~p-boundedness of maximal singular integral operators on product domains

By rotation method, Fourier transform estimates and LittlewoodPaley theory, the Lp boundedness of maximal singular integral operators with rough kernels on product domains is got. It is proved that if Ω∈Lq(Sn-1×Sm-1),q1,∫Sn-1Ω(x′,y′)dx′=0,y′∈Sm-1,∫Sm-1Ω(x′,y′)dy′=0,x′∈Sn-1,and b,h∈L∞(R1+), then the maximal singular integral operatorT*(f)=supe10,e20∫∫|u|e1|v|e2b(|u|)h(|v|)Ω(u′,v′)|v|n|v|mf(x-u,y-v)dudvis Lp bounded for 1p+∞. 