Journal of the
Korean Mathematical Society JKMS

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