The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ generated by the Littlewood-Paley operator [...] Mκ∗ 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∗ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,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).
@article{bwmeta1.element.doi-10_1515_math-2017-0110,
author = {Guanghui Lu and Shuangping Tao},
title = {Commutators of Littlewood-Paley [...] g k * $g\_{\kappa }^{*} $ -functions on non-homogeneous metric measure spaces},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1283-1299},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0110}
}
Guanghui Lu; Shuangping Tao. Commutators of Littlewood-Paley [...] g κ ∗ $g_{\kappa }^{*} $ -functions on non-homogeneous metric measure spaces. Open Mathematics, Tome 15 (2017) pp. 1283-1299. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0110/