Taiwanese Journal of Mathematics

Averaging Operators Along a Certain Type of Surfaces with Hypersingularity

Jin Bong Lee, Jongho Lee, and Chan Woo Yang

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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

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

First available in Project Euclid: 4 November 2019

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Digital Object Identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B15: Multipliers

singular integrals along surfaces oscillatory integrals hypersingularity Bessel functions


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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  • S. Chandarana, $L^p$-bounds for hypersingular integral operators along curves, Pacific J. Math. 175 (1996), no. 2, 389–416.
  • L. Grafakos, Classical Fourier Analysis, Second edition, Graduate Texts in Mathematics 249, Springer, New York, 2008.
  • N. Laghi and N. Lyall, Strongly singular integrals along curves, Pacific J. Math. 233 (2007), no. 2, 403–415.
  • E. M. Stein, Harmonic Analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series 43, Monographs in Harmonic Analysis III, Princeton University Press, Princeton, NJ, 1993.
  • E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295.
  • X. Wu and X. Yu, Strongly singular integrals along curves on $\alpha$-modulation spaces, J. Inequal. Appl. 2017 (2017), 185–197.