For any n ∈ ℕ, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space H¹(ℝⁿ). Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the H¹ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown to be valid on weighted Hardy spaces as well if the weights belong to the Muckenhoupt class A₁.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-5,
author = {Hussain Al-Qassem and Leslie Cheng and Yibiao Pan},
title = {Estimates for oscillatory singular integrals on Hardy spaces},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {277-289},
zbl = {1315.42009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-5}
}
Hussain Al-Qassem; Leslie Cheng; Yibiao Pan. Estimates for oscillatory singular integrals on Hardy spaces. Studia Mathematica, Tome 223 (2014) pp. 277-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-5/