WEIGHTED ESTIMATES FOR ROUGH SINGULAR INTEGRALS WITH APPLICATIONS TO ANGULAR INTEGRABILITY, II

This paper is devoted to studying certain singular integral operators with rough radial kernel h and sphere kernel Omega as well as the corresponding maximal operators along polynomial curves. The authors establish several weighted estimates for such operators by assuming that the kernels h (math)1 and Omega is an element of F-beta (Sn-1), or h is an element of Delta(gamma)(R+) and Omega is an element of W F-beta (Sn-1). Here F-beta (Sn-1) denotes the Grafakos-Stefanov kernel and W F-beta (Sn-1) denotes the variant of Grafakos-Stefanov kernel. As applications, the boundedness of such operators on the mixed radial-angular spaces (L vertical bar x vertical bar L theta q)-L-p(R-n) are obtained. Meanwhile, the corresponding vector-valued versions are also given. Moreover, the bounds are independent of the coefficients of the polynomials in the definition of operators.