arXiv subjects

Shaoxiong Hou

Publications and source records attributed to Shaoxiong Hou.

3 recordsLinked to original sources

arXiv2016

Orlicz addition for measures and an optimization problem for the $f$-divergence

In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional Orlicz-Brunn-Minkowski inequality, are established. We also investigate an optimization problem for the $f$-divergence and establish functional affine isoperimetric inequalities for the dual functional Orlicz affine and geominimal surface areas of measures.

math.MG↗

arXiv2014

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $φ: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a growth function such that $φ(x,\cdot)$ is nondecreasing, $φ(x,0)=0$, $φ(x,t)>0$ when $t>0$, $\lim_{t\to\infty}φ(x,t)=\infty$, and $φ(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_φ(\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the $φ$-Carleson measure characterization of the Musielak-Orlicz ${\mathop\mathrm{BMO}}$-type space $\mathop\mathrm{BMO}_φ(\mathbb{R}^n)$, which was proved to be the dual space of $H_φ(\mathbb{R}^n)$ by Luong Dang Ky.

math.CA↗

arXiv2014

Musielak-Orlicz BMO-Type Spaces Associated with Generalized Approximations to the Identity

Let $\mathcal{X}$ be a space of homogenous type and $φ:\ \mathcal{X}\times[0,\infty) \to[0,\infty)$ a growth function such that $φ(\cdot,t)$ is a Muckenhoupt weight uniformly in $t$ and $φ(x,\cdot)$ an Orlicz function of uniformly upper type 1 and lower type $p\in(0,1]$. In this article, the authors introduce a new Musielak-Orlicz BMO-type space $\mathrm{BMO}^φ_A(\mathcal{X})$ associated with the generalized approximation to the identity, give out its basic properties and establish its two equivalent characterizations, respectively, in terms of the spaces $\mathrm{BMO}^φ_{A,\,\mathrm{max}}(\mathcal{X})$ and $\widetilde{\mathrm{BMO}}^φ_A(\mathcal{X})$. Moreover, two variants of the John-Nirenberg inequality on $\mathrm{BMO}^φ_A(\mathcal{X})$ are obtained. As an application, the authors further prove that the space $\mathrm{BMO}^φ_{\sqrtΔ}(\mathbb{R}^n)$, associated with the Poisson semigroup of the Laplace operator $Δ$ on $\mathbb{R}^n$, coincides with the space $\mathrm{BMO}^φ(\mathbb{R}^n)$ introduced by L. D. Ky.

math.CA↗