$L^p\left(ℝⁿ\right)$ boundedness for the commutator of a homogeneous singular integral operator

Guoen Hu. "$L^{p}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator." Studia Mathematica 154.1 (2003): 13-27. <http://eudml.org/doc/284461>.

@article{GuoenHu2003,
abstract = {The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that $Ω ∈ L(log L)^\{k+1\}(S^\{n-1\})$ is a sufficient condition for the kth order commutator to be bounded on $L^\{p\}(ℝⁿ)$ for all 1 < p < ∞. The corresponding maximal operator is also considered.},
author = {Guoen Hu},
journal = {Studia Mathematica},
keywords = {commutator; singular integral operator; BMO; boundedness},
language = {eng},
number = {1},
pages = {13-27},
title = {$L^\{p\}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator},
url = {http://eudml.org/doc/284461},
volume = {154},
year = {2003},
}

TY - JOUR
AU - Guoen Hu
TI - $L^{p}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator
JO - Studia Mathematica
PY - 2003
VL - 154
IS - 1
SP - 13
EP - 27
AB - The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that $Ω ∈ L(log L)^{k+1}(S^{n-1})$ is a sufficient condition for the kth order commutator to be bounded on $L^{p}(ℝⁿ)$ for all 1 < p < ∞. The corresponding maximal operator is also considered.
LA - eng
KW - commutator; singular integral operator; BMO; boundedness
UR - http://eudml.org/doc/284461
ER -