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

Abstract 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 ˙ p β , q provided that Ω satisfies a size condition which contains the case Ω ∈ L r ( S n − 1 ) , r > 1 .