A van der Corput Type Lemma for Oscillatory Integrals with Holder Amplitudes and Its Applications
J. Korean Math. Soc. Published online November 25, 2020
Hussain Mohammed Al-Qassem, Leslie Cheng, and Yibiao Pan
Qatar University, Bryn Mawr College, University of Pittsburgh
Abstract : We prove a decay estimate for oscillatory integrals with Holder 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, Holder classes, Lp spaces, Lorentz spaces, Hardy spaces, singular integrals.