Boundedness of rough singular integral operators on the Triebel–Lizorkin spaces

We consider the singular integral operator T with kernel K(x) = Ω(x)/|x|n and prove its boundedness on the Triebel–Lizorkin spaces F˙ β,q p provided that Ω satisfies a size condition which contains the case Ω ∈ Lr (Sn−1), r >1. © 2007 Elsevier Inc. All rights reserved.