Rough oscillatory singular integrals on ℝⁿ

Hussain Mohammad Al-Qassem, Leslie Cheng, and Yibiao Pan. "Rough oscillatory singular integrals on ℝⁿ." Studia Mathematica 221.3 (2014): 249-267. <http://eudml.org/doc/285838>.

@article{HussainMohammadAl2014,
abstract = {We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.},
author = {Hussain Mohammad Al-Qassem, Leslie Cheng, Yibiao Pan},
journal = {Studia Mathematica},
keywords = {oscillatory singular integral; rough kernel; Orlicz spaces; block spaces; extrapolation},
language = {eng},
number = {3},
pages = {249-267},
title = {Rough oscillatory singular integrals on ℝⁿ},
url = {http://eudml.org/doc/285838},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Hussain Mohammad Al-Qassem
AU - Leslie Cheng
AU - Yibiao Pan
TI - Rough oscillatory singular integrals on ℝⁿ
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 3
SP - 249
EP - 267
AB - We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.
LA - eng
KW - oscillatory singular integral; rough kernel; Orlicz spaces; block spaces; extrapolation
UR - http://eudml.org/doc/285838
ER -