On the Triebel-Lizorkin space boundedness of Marcinkiewicz integrals along compound surfaces

In this paper the author present the boundedness of Marcinkiewicz integral operators associated to compound surfaces with rough kernels given by h ∈ Δγ(R+) and Ω ∈ L(log+ L)1/2(Sn−1)∪(∪1<r<∞B r (Sn−1)) on Triebel-Lizorkin spaces and Besov spaces. The main results of this paper represent improvements as well as natural extensions of many previously known results. Mathematics subject classification (2010): 42B20, 42B15, 47G10.