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http://dx.doi.org/10.4134/JKMS.j200155

A VAN DER CORPUT TYPE LEMMA FOR OSCILLATORY INTEGRALS WITH HÖLDER AMPLITUDES AND ITS APPLICATIONS  

Al-Qassem, Hussain (Department of Mathematics and Physics Qatar University)
Cheng, Leslie (Department of Mathematics Bryn Mawr College)
Pan, Yibiao (Department of Mathematics University of Pittsburgh)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 487-499 More about this Journal
Abstract
We prove a decay estimate for oscillatory integrals with Hölder 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; $H{\ddot{o}}lder$ classes; $L^p$ spaces; Lorentz spaces; Hardy spaces; singular integrals;
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