Related papers: Higher Order Riesz Transforms for Laguerre Expansi…

In this paper we represent the $k$-th Riesz transform in the ultraspherical setting as a principal value integral operator for every $k\in \mathbb{N}$. We also measure the speed of convergence of the limit by proving $L^p$-boundedness…

In the present paper, we establish that Riesz transforms for Dunkl Hermite expansion as introduced in [4] are singular integral operators with H\"ormander's type conditions and we show that are bounded on $L^p(\mathbb{R}^d; d\mu_k) 1 < p <…

In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of…

Let $\nu=(\nu_1,\ldots,\nu_n)\in (-1,\infty)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 +…

In this paper we study higher order Riesz transforms associated with the inverse Gaussian measure given by $\pi ^{n/2}e^{|x|^2}dx$ on $\mathbb{R}^n$. We establish $L^p(\mathbb{R}^n,e^{|x|^2}dx)$-boundedness properties and obtain…

On $\mathbb{R}^d_+$, endowed with the Laguerre probability measure $\mu_\alpha$, we define a Hodge-Laguerre operator $\mathbb{L}_\alpha=\delta\delta^*+\delta^* \delta$ acting on differential forms. Here $\delta$ is the Laguerre exterior…

In this paper we establish $L^p$-boundedness properties for variation, oscillation and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.

We prove the $L^p$-boundedness for all $p \in (1,\infty)$ of the first-order Riesz transforms $X_j \mathcal{L}^{-1/2}$ associated with the Laplacian $\mathcal{L} = -\sum_{j=0}^n X_j^2$ on the $ax+b$-group $G = \mathbb{R}^n \rtimes…

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transfer- ence theorems, we deduce boundedness theorems for Riesz…

We study the boundedness of Riesz transforms in $L^p$ for $p>2$ on a doubling metric measure space endowed with a gradient operator and an injective, $\omega$-accretive operator $L$ satisfying Davies-Gaffney estimates. If $L$ is…

In this paper we establish the $L^p$-boundedness properties of the variation operators associated with the heat semigroup, Riesz transforms and commutator between Riesz transforms and multiplication by $BMO(R^n)$-functions in the…

Let \(\mathcal{L}_\nu\) be the Laguerre differential operator which is the self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2} \left(\nu_i^2 -…

In this paper, we provide the boundedness property of the Riesz transforms associated to the Schr\"odinger operator $\mathcal{L}=-\Delta + \mathbf{V}$ in a new weighted Morrey space which is the generalized version of many previous Morrey…

Let $\Delta = \nabla^* \nabla$ be the distinguished Laplacian on a Damek-Ricci space. We prove the $L^{p}$-boundedness of the vector of first-order Riesz transforms $\nabla \Delta^{-1/2}$ in the full range $p\in(1,\infty)$. The most…

Let $\nu=(\nu_1,\ldots,\nu_n)\in (-1,\vc)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2}(\nu_i^2 -…

Let $L=-\Delta +|x|^2$ be the Hermite operator on $\mathbb{R}^n$, and $T$ be a Calder\'on-Zygmund type operator that is modelled on certain singular integrals related to $L$. We establish necessary and sufficient conditions for $T$ to be…

Let $\nu\in [-1/2,\infty)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2}(\nu_i^2 -…

For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.

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…

In this paper, we establish sufficient conditions for a singular integral $T$ to be bounded from certain Hardy spaces $H^p_L$ to Lebesgue spaces $L^p$, $0< p \le 1$, and for the commutator of $T$ and a BMO function to be weak-type bounded…