Results 1 to 10 of about 16 (16)
Analysis and Geometry in Metric Spaces, 2022 Let (𝒳, d, μ) be a non-homogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. Under assumption that θ and dominating function λ satisfy certain conditions, the authors prove that ...
Lu Guanghui +2 more
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Some estimates for commutators of Littlewood-Paley g-functions
Open Mathematics, 2021 The aim of this paper is to establish the boundedness of commutator [b,g˙r]\left[b,{\dot{g}}_{r}] generated by Littlewood-Paley gg-functions g˙r{\dot{g}}_{r} and b∈RBMO(μ)b\in {\rm{RBMO}}\left(\mu ) on non-homogeneous metric measure space.
Lu Guanghui
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Analysis and Geometry in Metric Spaces, 2023 Let (X,d,μ)\left({\mathcal{X}},d,\mu ) be a non-homogeneous metric measure space satisfying the geometrically doubling and upper doubling conditions. In this setting, we first introduce a generalized Morrey space Mpu(μ){M}_{p}^{u}\left(\mu ), where 1 ...
Lu Guanghui +2 more
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Almost uniform domains and Poincaré inequalities
Transactions of the London Mathematical Society, 2021 Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure.
Sylvester Eriksson‐Bique, Jasun Gong
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Isoperimetric and Poincaré Inequalities on Non-Self-Similar Sierpiński Sponges: the Borderline Case
Analysis and Geometry in Metric Spaces, 2022 In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more ...
Eriksson-Bique Sylvester, Gong Jasun
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Admissibility versus Ap-Conditions on Regular Trees
Analysis and Geometry in Metric Spaces, 2020 We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.
Nguyen Khanh Ngoc, Wang Zhuang
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Fractional type Marcinkiewicz integrals over non-homogeneous metric measure spaces
Journal of Inequalities and Applications, 2016 The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integral M β , ρ , q $\mathcal{M}_{\beta,\rho,q}$ on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling ...
Guanghui Lu, Shuangping Tao
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Open Mathematics, 2017 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 ...
Lu Guanghui, Tao Shuangping
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Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
Analysis and Geometry in Metric Spaces, 2013 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
Balogh Zoltán M. +2 more
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Analysis and Geometry in Metric Spaces, 2018 We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincaré inequality.
Lahti Panu +2 more
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