Singular integrals with non-standard kernels on Triebel-Lizorkin spaces

Phong and Stein introduced a class of non-standard singular integral operators with mixed homogeneities.Han, Krantz and Tan studied these non-standard convolution singular integrals and establish the boundedness of these singular integrals on the Hardy spaces.The purpose of this paper is to prove that the non-standard singular integral operators are bounded on Triebel-Lizorkin spaces.