Singular Integral Operators with Rough Kernel on Function Spaces Over Local Fields

In this article we study the boundedness of classical singular integral operator over local fields with rough kernel. We are relaxing the smoothness condition on kernel by block spaces and found the boundedness of truncated singular integral operator on different function spaces such as Lebesgue spaces, Besov spaces and Triebel-Lizorkin spaces. Unlike Euclidean space, our bound of truncated singular integral operator depends on the constant which leads the unboundedness of singular integral operator over local fields.