使用Bessel卷积刻画取值于Banach空间的BMO函数与UMD Banach空间

Bessel 框架下的 BMO 函数与 Carleson 测度的 Balayage

BMO functions and Balayage of Carleson measures in the Bessel setting

本文将 Bessel 框架下具有有界支撑的奇 BMO 函数刻画为有界函数与 Carleson 测度关于 Bessel 算子相关 Poisson 半群的 balayage 之和，推广了 Carleson 的经典结果。

UMD Banach空间与几个算子平方根的极大正则性

UMD Banach spaces and the maximal regularity for the square root of several operators

本文证明了与Hermite、Bessel或Laguerre型算子平方根相关的Cauchy问题的极大$L^p$-正则性可刻画Banach空间$X$的UMD性质。

Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting

Fix $λ>0$. Consider the Hardy space $H^1(\mathbb{R}_+,dm_λ)$ in the sense of Coifman and Weiss, where $\mathbb{R_+}:=(0,\infty)$ and $dm_λ:=x^{2λ}dx$ with $dx$ the Lebesgue measure. Also consider the Bessel operators $Δ_λ:=-\frac{d^2}{dx^2}-\frac{2λ}{x} \frac d{dx}$, and $S_λ:=-\frac{d^2}{dx^2}+\frac{λ^2-λ}{x^2}$ on $\mathbb{R_+}$. The Hardy spaces $H^1_{Δ_λ}$ and $H^1_{S_λ}$ associated with $Δ_λ$ and $S_λ$ are defined via the Riesz transforms $R_{Δ_λ}:=\partial_x (Δ_λ)^{-1/2}$ and $R_{S_λ}:= x^λ\partial_x x^{-λ} (S_λ)^{-1/2}$, respectively. It is known that $H^1_{Δ_λ}$ and $H^1(\mathbb{R}_+,d…

Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrödinger operators

In this paper we establish the product Hardy spaces associated with the Bessel Schrödinger operator introduced by Muckenhoupt and Stein, and provide equivalent characterizations in terms of the Bessel Riesz transforms, non-tangential and radial maximal functions, and Littlewood--Paley theory, which are consistent with the classical product Hardy space theory developed by Chang and Fefferman. Moreover, in this specific setting, we also provide another characterization via the Telyakovskií transform, which further implies that the product Hardy space associated with this Bessel Schrödinger opera…

可由 BMO 函数的 Bessel Poisson 积分表示的 Weinstein 方程的解

Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

本文研究了区间上的 Weinstein 型方程，将可由 BMO 函数的 Bessel-Poisson 积分表示的解，刻画为满足特定 Carleson 性质的解。

Hardy空间、Campanato空间与Bessel算子相关的高阶Riesz变换

Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators

本文针对多元Bessel算子$Δ_ν$，建立了相关Hardy空间与BMO型空间理论，证明其高阶Riesz变换为Calderón-Zygmund算子且在上述空间上有界，推进了Bessel算子框架下的调和分析研究。

在Bessel设定下利用Carleson测度刻画一致凸与光滑Banach空间

Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings

本文利用由Bessel算子和Banach值BMO函数相关Poisson积分定义的Carleson测度，给出了q一致凸与光滑Banach空间的新刻画，并通过Lusin积分的映射性质描述其一致凸性与光滑性。

Compactness of Riesz transform commutator associated with Bessel operators

Let $λ>0$ and $\triangle_λ:=-\frac{d^2}{dx^2}-\frac{2λ}{x} \frac d{dx}$ be the Bessel operator on $\mathbb R_+:=(0,\infty)$. We first introduce and obtain an equivalent characterization of ${\rm CMO}(\mathbb R_+,\, x^{2λ}dx)$. By this equivalent characterization and establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function $b\in {\rm BMO}(\mathbb R_+,\, x^{2λ}dx)$ is in ${\rm CMO}(\mathbb R_+,\, x^{2λ}dx)$ if and only if the Riesz transform commutator $[b, R_{Δ_λ}]$ is compact on $L^p(\mathbb R_+, x^{2λ}dx)$ for any $p\in(1, \infty)$.

贝塞尔里斯变换及其与Andersen–Kerman权的交换子的精确加权估计

Sharp weighted estimates for the Bessel Riesz transform and its commutator with Andersen--Kerman weights

本文针对贝塞尔里斯变换及其与Andersen–Kerman权的交换子，证明了对应的精确定量加权估计，解决了此前未解决的相关精确加权界问题。

Approximation in the Zygmund and Hölder classes on $\mathbb{R}^n$

We determine the distance (up to a multiplicative constant) in the Zygmund class $Λ_{\ast}(\mathbb{R}^n)$ to the subspace $\mathrm{J}(\mathbf{bmo})(\mathbb{R}^n).$ The latter space is the image under the Bessel potential $J := (1-Δ)^{-1/2}$ of the space $\mathbf{bmo}(\mathbb{R}^n),$ which is a non-homogeneous version of the classical $\mathrm{BMO}.$ Locally, $\mathrm{J}(\mathbf{bmo})(\mathbb{R}^n)$ consists of functions that together with their first derivatives are in $\mathbf{bmo}(\mathbb{R}^n).$ More generally, we consider the same question when the Zygmund class is replaced by the Hölder s…

Boundedness of differential transforms for Poisson semigroups generated by Bessel operators

In this paper we analyze the convergence of the following type of series \begin{equation*} T_N f(x)=\sum_{j=N_1}^{N_2} v_j\Big(\mathcal{P}_{a_{j+1}} f(x)-\mathcal{P}_{a_{j}} f(x)\Big),\quad x\in \mathbb R_+, \end{equation*} where $\{\mathcal{P}_t \}_{t>0}$ is the Poisson semigroup of the Bessel operator $\displaystyle Δ_λ:=-{d^2\over dx^2}-{2λ\over x}{d\over dx}$ with $λ$ being a positive constant, $N=(N_1, N_2)\in \mathbb Z^2$ with $N_1<N_2,$ $\{v_j\}_{j\in \mathbb Z}$ is a bounded real sequences and $\{a_j\}_{j\in \mathbb Z}$ is an increasing real sequence. {Our analysis will consist in the …

Bessel 情形中的 Muckenhoupt 型权函数与内在结构

Muckenhoupt-type weights and the intrinsic structure in Bessel Setting

本文研究 Bessel 算子框架下的 Muckenhoupt 型权函数，提出刻画极大函数加权有界性的新权类 $\widetilde A_{p,λ}$，并证明 Bessel Riesz 变换交换子的加权有界性等价于 $b$ 属于关联 BMO 空间。

带Andersen--Kerman权的Bessel Riesz变换的双权交换子

Two-weight commutators for the Bessel Riesz transform with Andersen--Kerman weights

本文刻画了带Andersen--Kerman权的Bessel Riesz变换交换子的有界性与紧性，建立了其与BMO_{ν,α}、VMO_{ν,α}的等价关系，采用共轭方法转化问题并推导相关估计。

Pointwise multiplication on vector-valued function spaces with power weights

We investigate pointwise multipliers on vector-valued function spaces over $\mathbb{R}^d$, equipped with Muckenhoupt weights. The main result is that in the natural parameter range, the characteristic function of the half-space is a pointwise multiplier on Bessel-potential spaces with values in a UMD Banach space. This is proved for a class of power weights, including the unweighted case, and extends the classical result of Shamir and Strichartz. The multiplication estimate is based on the paraproduct technique and a randomized Littlewood-Paley decomposition. An analogous result is obtained fo…