Abstract
In this paper we obtain almost sharp decay estimates for $L^2$ operator norm of strongly singular oscillatory integral operators in $\mathbb{R}^{n+1}$ for $n \geq 2$; we prove some necessary condition for $L^2$ estimates. Also, we prove that the operators are bounded on $L^p$ for some $p \neq 2$ and the range of $p$ depends on the hypersingularity of the operators.
Citation
Jin Bong Lee. Jongho Lee. Chan Woo Yang. "Averaging Operators Along a Certain Type of Surfaces with Hypersingularity." Taiwanese J. Math. 24 (2) 317 - 329, April, 2020. https://doi.org/10.11650/tjm/191101
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