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

100%

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).

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

84%

Balogh Z. M., Tyson J. T., Wildrick K.

Analysis and Geometry in Metric Spaces

2013

tom 1

232-254

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Open Mathematics

1 Balogh Z. M.

1 Lu G.

1 Tao S.

1 Tyson J. T.

1 Wildrick K.

1 2017

1 2013

Wyniki wyszukiwania

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

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces