Averaging Operators Along a Certain Type of Surfaces with Hypersingularity

초록

In this paper we obtain almost sharp decay estimates for L-2 operator norm of strongly singular oscillatory integral operators in Rn+1 for n >= 2; we prove some necessary condition for L-2 estimates. Also, we prove that the operators are bounded on LP for some p not equal 2 and the range of p depends on the hypersingularity of the operators.

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