## Taiwanese Journal of Mathematics

### 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 $\mathbb{R}^{n+1}$ 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.

#### Article information

Source
Taiwanese J. Math., Advance publication (2019), 13 pages.

Dates
First available in Project Euclid: 4 November 2019

https://projecteuclid.org/euclid.twjm/1572836421

Digital Object Identifier
doi:10.11650/tjm/191101

#### Citation

Lee, Jin Bong; Lee, Jongho; Yang, Chan Woo. Averaging Operators Along a Certain Type of Surfaces with Hypersingularity. Taiwanese J. Math., advance publication, 4 November 2019. doi:10.11650/tjm/191101. https://projecteuclid.org/euclid.twjm/1572836421

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