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

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1283-1299
- ISSN: 2391-5455

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topGuanghui 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 -

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