Related papers: Triebel-Lizorkin spaces in Dunkl setting

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel--Lizorkin-type spaces $\dot B^{s,\tau}_{p,q}(W)$ and $\dot F^{s,\tau}_{p,q}(W)$. In this article, the authors establish the molecular…

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…

This article gives general results on invariance of anisotropic Lizorkin--Triebel spaces with mixed norms under coordinate transformations on Euclidean space, open sets and cylindrical domains.

We present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincar\'e groups, together with their Spin double covers, by means of Mackey's theory of induced representations for…

We give a complete characterisation of the spaces $\dot{B}^{\alpha}_{p,q}$ and $\dot{F}^{\alpha}_{p,q}$ by using a non-smooth kernel satisfying near minimal conditions. The tools used include a Stromberg-Torchinsky type estimate for certain…

The Dunkl total angular momentum algebra (TAMA) is realised as the dual partner of the orthosymplectic Lie superalgebra containing the Dunkl deformation of the Dirac operator. In this paper, we consider the case when the reflection group…

A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel-Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases…

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation…

Motivated by the results of Korry and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show…

In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness of their commutator with respect to the central BMO space…

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

Kuelbs-Steadman spaces are introduced in this article on a separable metric space with finite diameter and finite positive Borel measure. Kuelbs-Steadman spaces of the Lipschitz type are also discussed. Various inclusion properties are also…

In the setting of $\R^d$ with an $n-$dimensional measure $\mu,$ we give several characterizations of Lipschitz spaces in terms of mean oscillations involving $\mu.$ We also show that Lipschitz spaces are preserved by those Calderon-Zygmund…

We introduce the homogeneous (inhomogeneous) matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces and obtain their equivalent norms. We also obtain their characterizations by Peetre type maximal functions, Lusin-area function,…

The aim of this paper is to prove duality of Triebel-Lizorkin spaces $% F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }$. First, we prove the duality of associated sequence spaces. Then from the so-called $% \varphi $-transform…

Consider the discrete Laplacian $\Delta_d$ defined on the set of integers $\mathbb Z$ by \[ \Delta_d f(n) = -f(n+1) + 2f(n) -f(n-1), \ \ \ \ n\in \mathbb Z, \] where $f$ is a function defined on $\mathbb Z$. In this paper, we define Hardy…

We characterize the Hardy space $H^1$ in the rational Dunkl setting associated with the reflection group $\mathbb Z_2^n$ by means of Riesz transforms. As a corollary we obtain a Riesz transform characterization of $H^1$ for product of…

Let $\Delta$ and $L=\Delta -\|\mathbf x\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal…

Using Dunkl theory, we introduce into consideration some weighted $L_p$-spaces on $[-1,1]$ and on the unit Euclidean sphere $\mathbb{S}^{d-1}$, $d\geq 2$. Then we define a family of linear bounded operators $\{V_\kappa^p(x)\colon…

Let $(X,\mu)$ be a space of homogeneous type satisfying $\mu(X) =\infty$, the doubling property and the reverse doubling condition. Let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel enjoys a Gaussian upper bound.…