Lp Boundedness of Fourier Integral Operators in the Class S1,0

We prove the following properties: (1) Let a is an element of Lambda(m0)(1,0,k,k') (R-n x R-n) with m(0) = -1 vertical bar 1/p - 1/2 vertical bar(n - 1), n >= 2 (1 < p <= 2, k > n/p, k' > 0; 2 <= p <= infinity, k > n/2, k' > 0 respectively). Suppose the phase function S is positively homogeneous in xi-variables, non-degenerate and satisfies certain conditions. Then the Fourier integral operator T is L-p-bounded. Applying the method of (1), we can obtain the L-p-boundedness of the Fourier integral operator if (2) the symbol a is an element of Lambda(1,delta,k,k'), 0 <= delta < 1, with m(0), k, k' and S given as in (1). Also, the method of (1) gives: (3) a is an element of Lambda(1,delta,k,k'),(0) 0 <= delta < 1 and k, k' given as in (1), then the L-p-boundedness of the pseudo-differential operators holds, 1 < p < infinity.