Sharp bounds for oscillatory singular integrals on Hardy spaces
Volume 238 / 2017
Studia Mathematica 238 (2017), 121-132
MSC: Primary 42B20; Secondary 42B30.
DOI: 10.4064/sm8496-2-2017
Published online: 21 April 2017
Abstract
We establish the optimal bound for oscillatory singular integrals with polynomial phase functions of arbitrary degrees on the Hardy space $H^1(\mathbb {R}^n)$. We also prove that such a bound remains valid in the setting of weighted Hardy spaces.
