A CLASS OF OSCILLATORY SINGULAR INTEGRALS ON TRIEBEL-LIZORKIN SPACES

. The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e i|x|a Ω(x)|x| -n is studied,where a∈R,a≠0,1 and Ω∈L1(S n-1 ) is homogeneous of degree zero and satisfies certain cancellation condition.When kernel Ω(x′)∈Llog+L(S n-1 ),the α,q _ p (Rn) boundedness of the above operator is obtained.Meanwhile,when Ω(x) satisfies L1-Dini condition,the above operator T is bounded on 0,1 _ 1 (Rn).