Mapping properties of fundamental operators in harmonic analysis related to Bessel operators

On the Harmonic Analysis Associated to the Bessel-Struve Operator

In this paper, we introduce the Bessel-Struve transform, we establish an inversion theorem of the Weyl integral transform associated with this transform, in the case of half integers, we give a characterization of the range of $\mathcal{D}(\mathbb{R})$ by Bessel-Struve transform and we prove a Schwartz-Paley-Wiener theorem on $\mathcal{E}'(\mathbb{R})$.

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

We prove sharp power-weighted $L^p$, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator $B_ν$ in the exotic range of the parameter $-\infty < ν< 1$. Moreover, in the same framework, we characterize basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical $g$-function and fractional integrals (Riesz potential operators).

Quantitative weighted estimates for harmonic analysis operators in the Bessel setting by using sparse domination

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in terms of the $A_p$-characteristic of the weight $w$. In order to do this we show that the operators under consideration are dominated by a suitable family of sparse operators in the space of homogeneous type $((0,\infty),|\cdot |,x^{2λ}dx)$.

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。

与多维 Bessel 算子相关的调和分析算子

Harmonic Analysis Operators Associated with Multidimensional Bessel Operators

本文研究了多维 Bessel 算子相关的调和分析算子，证明了热半群的极大算子和 Littlewood-Paley g-函数的弱型(1,1)性质，以及 Riesz 变换的强型(p,p)和弱型(1,1)有界性。

Bessel 背景下的 Calderón-Zygmund 算子

Calderón-Zygmund operators in the Bessel setting

本文研究了 Bessel 算子相关的调和分析基本算子，证明其为齐次型空间意义下的 Calderón-Zygmund 算子，从而由一般理论导出其映射性质。