Convergence of truncated rough singular integrals supported by subvarieties on Triebel-Lizorkin spaces

摘要

Let be a function of homogeneous of degree zero and satisfy the cancellation condition on the unit sphere. Suppose that h is a radial function. Let be the classical singular Radon transform, and let be its truncated operator with rough kernels associated to polynomial mapping , which is defined by . In this paper, we show that for any (-, ) and (p, q) satisfying certain index condition, the operator enjoys the following convergence properties and , provided that L(log(+)L)(Sn-1) for some ( 0, 1], or H-1(Sn-1), or (1qBq(0,0)(Sn-1)).