In this paper we obtain almost sharp decay estimates for L2 operator norm of strongly singular oscillatory integral operators in ℝn+1 for n ≥ 2; we prove some necessary condition for L2 estimates. Also, we prove that the operators are bounded on Lp for some p ≠ 2 and the range of p depends on the hypersingularity of the operators.
- Oscillatory integrals
- Singular integrals along surfaces
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