Averaging Operators Along a Certain Type of Surfaces with Hypersingularity

Abstract

In this paper we obtain almost sharp decay estimates for L 2 operator norm of strongly singular oscillatory integral operators in R n+1 for n ≥ 2; we prove some necessary condition for L 2 estimates. Also, we prove that the operators are bounded on L p for some p = 2 and the range of p depends on the hypersingularity of the operators.