Commutators of Littlewood-Paley [...] g κ ∗ $g_{\kappa }^{*}$ -functions on non-homogeneous metric measure spaces

Guanghui Lu, and Shuangping Tao. "Commutators of Littlewood-Paley [...] g κ ∗ $g_{\kappa }^{*} $ -functions on non-homogeneous metric measure spaces." Open Mathematics 15.1 (2017): 1283-1299. <http://eudml.org/doc/288355>.

@article{GuanghuiLu2017,
abstract = {The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ $\mathcal \{M\}_\{\kappa ,b\}^\{*\} $ generated by the Littlewood-Paley operator [...] Mκ∗ $\mathcal \{M\}_\{\kappa \}^\{*\} $ and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of [...] Mκ∗ $\mathcal \{M\}_\{\kappa \}^\{*\} $ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ $\mathcal \{M\}_\{\kappa ,b\}^\{*\} $ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from the space L log L(μ) to the weak Lebesgue space L1,∞(μ), and is bounded from the atomic Hardy spaces H1(μ) to the weak Lebesgue spaces L1,∞(μ).},
author = {Guanghui Lu, Shuangping Tao},
journal = {Open Mathematics},
keywords = {Non-homogeneous metric measure space; Commutators; gκ*-functions; RBMO (μ); Hardy space},
language = {eng},
number = {1},
pages = {1283-1299},
title = {Commutators of Littlewood-Paley [...] g κ ∗ $g_\{\kappa \}^\{*\} $ -functions on non-homogeneous metric measure spaces},
url = {http://eudml.org/doc/288355},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Guanghui Lu
AU - Shuangping Tao
TI - Commutators of Littlewood-Paley [...] g κ ∗ $g_{\kappa }^{*} $ -functions on non-homogeneous metric measure spaces
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1283
EP - 1299
AB - The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ $\mathcal {M}_{\kappa ,b}^{*} $ generated by the Littlewood-Paley operator [...] Mκ∗ $\mathcal {M}_{\kappa }^{*} $ and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of [...] Mκ∗ $\mathcal {M}_{\kappa }^{*} $ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ $\mathcal {M}_{\kappa ,b}^{*} $ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from the space L log L(μ) to the weak Lebesgue space L1,∞(μ), and is bounded from the atomic Hardy spaces H1(μ) to the weak Lebesgue spaces L1,∞(μ).
LA - eng
KW - Non-homogeneous metric measure space; Commutators; gκ*-functions; RBMO (μ); Hardy space
UR - http://eudml.org/doc/288355
ER -