Abstract
In this paper the authors prove that the homogeneous singular integral T Ω with Ω ∈ H 1 ( S n − 1 ) is bounded on the Triebel–Lizorkin spaces and the Besov spaces. These results answer an open problem proposed by Chen and Zhang in [J. Chen, C. Zhang, Boundedness of rough singular integral on the Triebel–Lizorkin spaces, J. Math. Anal. Appl. 337 (2008) 1048–1052]. The same results hold also for the rough singular integral operators T Ω , h with radial function kernels.
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