J. Korean Math. Soc. 2021; 58(2): 487-499
Online first article November 25, 2020 Printed March 1, 2021
https://doi.org/10.4134/JKMS.j200155
Copyright © The Korean Mathematical Society.
Hussain Al-Qassem, Leslie Cheng, Yibiao Pan
Qatar University; Bryn Mawr College; University of Pittsburgh
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
1998; 35(2): 295-314
2005; 42(1): 111-127
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