A van der Corput type lemma for oscillatory integrals with H\"older amplitudes and its applications
J. Korean Math. Soc. 2021 Vol. 58, No. 2, 487-499
https://doi.org/10.4134/JKMS.j200155
Published online November 25, 2020
Printed March 1, 2021
Hussain Al-Qassem, Leslie Cheng, Yibiao Pan
Qatar University; Bryn Mawr College; University of Pittsburgh
Abstract : We prove a decay estimate for oscillatory integrals with \linebreak H\"older amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.
Keywords : van der Corput's lemma, oscillatory integrals, H\"older classes, $L^p$ spaces, Lorentz spaces, Hardy spaces, singular integrals
MSC numbers : Primary 42B20; Secondary 42B30, 42B35
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