Estimates for oscillatory singular integrals on Hardy spaces

Hussain Al-Qassem, Leslie Cheng, and Yibiao Pan. "Estimates for oscillatory singular integrals on Hardy spaces." Studia Mathematica 224.3 (2014): 277-289. <http://eudml.org/doc/286623>.

@article{HussainAl2014,
abstract = {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.},
author = {Hussain Al-Qassem, Leslie Cheng, Yibiao Pan},
journal = {Studia Mathematica},
keywords = {oscillatory integrals; singular integrals; Hardy spaces},
language = {eng},
number = {3},
pages = {277-289},
title = {Estimates for oscillatory singular integrals on Hardy spaces},
url = {http://eudml.org/doc/286623},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Hussain Al-Qassem
AU - Leslie Cheng
AU - Yibiao Pan
TI - Estimates for oscillatory singular integrals on Hardy spaces
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 3
SP - 277
EP - 289
AB - 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.
LA - eng
KW - oscillatory integrals; singular integrals; Hardy spaces
UR - http://eudml.org/doc/286623
ER -