$L^p$ estimates for angular maximal functions associated with Stieltjes and Laplace transforms

移位渐近展开中的Appell多项式：Mills比率、Hermite多项式与Stieltjes界

Appell Polynomials in Shifted Asymptotic Expansions: the Mills ratio, Hermite polynomials, and Stieltjes bounds

本文扩展了移位渐近展开的Appell多项式构造，建立了Borel-Laplace表示，推导了Mills-Hermite展开的余项估计与有限差分公式，将其应用于非中心高斯尾展开，并得到Stieltjes矩序列对应的双侧界层级。

Nielsen's beta function and some infinitely divisible distributions

We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form $xf(x)$, where $f$ is itself the Laplace transform of a sum of dilations and translations of periodic functions. Our methods are also applied to ratios of Gamma functions, and to the remainders in asymptotic expansions of the double Gamma function of Barnes.

Harmonic analysis operators related to symmetrized Jacobi expansions

Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators, including Riesz transforms, Poisson semigroup maximal operator, Littlewood-Paley-Stein square functions and multipliers of Laplace and Laplace-Stieltjes transform type. Our paper delivers also some new results in the original setting of classical Jacobi expansions.

Calderón-Zygmund operators related to Laguerre function expansions of convolution type

We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $α$ in this context. This generalizes a simpler method existing in the literature, but being valid for a restricted range of $α$. As an application, we prove that several fundamental operators in harmonic analysis of the Laguerre expansions, including maximal operators related to the heat and Poisson semigroups, Riesz transforms, Littlewood-Paley-Stein type square functions and multipliers of Laplace and Laplace-Stieltjes tra…

$q$-Laplace变换的比较：基本的连通超几何函数${}_2ϕ_0$

The $q$-Laplace Transforms compared: the basic confluent hypergeometric function ${}_2ϕ_0$

本文比较了三种$q$-Laplace变换方法，推导了${}_2ϕ_0$函数的反演方法及其性质，揭示了$q$-指数小差异的显式公式。

所有可能类型指标下 Bessel 背景中的 Calderón-Zygmund 算子

Calderón-Zygmund operators in the Bessel setting for all possible type indices

本文改编已有技术，证明 Bessel 背景下的极大算子、平方函数及 Riesz 变换等调和分析算子在所有可能的类型参数 $λ$ 下均为 Calderón-Zygmund 算子，扩展了此前仅适用于受限范围的结果。

On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings

We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calderón-Zygmund theory we prove that these operators are bounded on weighted $L^p$ spaces, $1 < p < \infty$, and from weighted $L^1$ to weighted weak $L^1$. …

关于特定 Dunkl 和 Bessel 背景下的基本调和分析算子

On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

本文在反射群同构于 $\mathbb{Z}_2^n$ 的 Dunkl Laplacian 多维背景下，研究了极大算子、$g$-函数、Riesz 变换等调和分析算子，并运用 Calderón-Zygmund 理论证明了其在加权 $L^p$ 空间及弱 $L^1$ 空间的有界性。

齐次树上与拉普拉斯算子相关的热半群及其子ordinated族的逐点收敛性与两个加权$L^p$极大不等式

Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted $L^p$ maximal inequalities

本文刻画齐次树上热半群及其子ordinated族逐点收敛的权函数条件，并证明该收敛等价于相应极大算子的加权$L^p$有界性。

最大型整函数的指示图理论及解析延拓性的刻画

The indicator diagram theory for maximal type entire functions and the characterization of analytic continuability

通过引入扩展复平面，将Pólya指示图理论推广至阶数≤1的最大型整函数，建立Laplace变换及其逆变换，并证明Pólya定理的类比，进而推广幂级数解析延拓性的刻画。

A higher rank Racah algebra and the $\mathbb{Z}_2^{n}$ Laplace-Dunkl operator

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the $n$-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy-Kovalevskaia theorem. These bases consist of joint eigenfunctions of maximal Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on the…

抛物型 Muckenhoupt 类的刻画

Characterizations of parabolic Muckenhoupt classes

本文利用带时间滞后的非中心抛物型极大函数刻画极限抛物型 A_∞ 与 A_1 类，并借助 Calderón-Zygmund 分解等论证扩展抛物型 Muckenhoupt 权理论。

Radial Maximal Function Characterizations of Hardy Spaces on RD-Spaces and Their Applications

Let ${\mathcal X}$ be an RD-space with $μ({\mathcal X})=\infty$, which means that ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we characterize the atomic Hardy spaces $H^p_{\rm at}(\{\mathcal X})$ of Coifman and Weiss for $p\in(n/(n+1),1]$ via the radial maximal function, where $n$ is the "dimension" of ${\mathcal X}$, and the range of index $p$ is the best possible. This completely answers the question proposed by Ronald R. Coifman and Guido Weiss in 1977 in this setting, and improves on a dee…

Localized BMO and BLO Spaces on RD-Spaces and Applications to Schrödinger Operators

An RD-space ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling condition holds in ${\mathcal X}$. Let $ρ$ be an admissible function on RD-space ${\mathcal X}$. The authors first introduce the localized spaces $\mathrm{BMO}_ρ({\mathcal X})$ and $\mathrm{BLO}_ρ({\mathcal X})$ and establish their basic properties, including the John-Nirenberg inequality for $\mathrm{BMO}_ρ({\mathcal X})$, several equivalent characterizations for $\mathrm{BLO}_ρ({\mathcal X})$, and some relations between these spaces. Then the author…