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

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Lu G., Tao S.

Open Mathematics

2017

tom 15

nr 1

1283-1299

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).

Ograniczanie wyników

1 Open Mathematics

1 Lu G.

1 Tao S.

1 2017

Wyniki wyszukiwania

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