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 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.j200155Published online November 25, 2020Printed 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 Downloads: Full-text PDF   Full-text HTML