Related papers: Hardy spaces for Bessel-Schr\"odinger operators

Let $L_{1}$ and $L_{2}$ be non-negative self-adjoint operators acting on $L^{2}(X_{1})$ and $L^{2}(X_{2})$, respectively, where $X_{1}$ and $X_{2}$ are spaces of homogeneous type. Assume that $L_{1}$ and $L_{2}$ have Gaussian heat kernel…

In this paper, we investigate a class of fractional Hardy type operators $\mathscr{H}_{\beta_{1},\cdots,\beta_{m}}$ defined on higher-dimensional product spaces…

We study the holomorphic Hardy-Orlicz spaces H^\Phi(\Omega), where \Omega is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function \Phi is in particular such that H…

Given a holomorphic self-map $\varphi$ of $\D$ (the open unit disc in $\mathbb{C}$), the composition operator $C_{\varphi} f = f \circ \varphi$, $f \in H^2(\mathbb{\D})$, defines a bounded linear operator on the Hardy space…

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…

In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calder\'on-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces $(X,…

Let a:[0,1] -> R be a Lebesgue-almost everywhere positive function. We consider the Riemann-Liouville operator R^a of variable order a(.) as an operator from L_p[0,1] to L_q[0,1]. Our first aim is to study its continuity properties. For…

We consider the invariant subspace of composition operators on Hardy space $H^p$ where the composition operators corresponding to a function $\varphi$ that is a holomorphic self-map of $\mathbb D$. Firstly, we discuss composition operators…

Let $n\ge 1$ and $\varphi: \mathbb{D}^n\to\mathbb{D}$ be a holomorphic function, where $\mathbb{D}$ denotes the open unit disk of $\mathbb{C}$. Let $\Theta: \mathbb{D} \to \mathbb{D}$ be an inner function and $K^p_\Theta$, $p>0$, denote the…

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

For $0<p<\infty $ and $\alpha >-1$ the space of Dirichlet type $\mathcal D^p_\alpha $ consists of those functions $f$ which are analytic in the unit disc $\mathbb D$ and satisfy $\int_{\mathbb D}(1-| z| )^\alpha| f^\prime (z)|…

In this article, we obtain some necessary and sufficient conditions for the boundedness of fractional Hausdorff operators $h_{\Phi,\beta}$ on weighted Lebesgue spaces $(0\leq\beta<1)$, which are fractional variants of Bandaliev-Safarova…

In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $\mathcal…

In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…

This paper provides a study of problems related to Hardy spaces left by G.\,Weiss in \cite{We}. First, We will prove that the Hardy spaces $H^p(\mathbb{R}^n)$ can be characterized by a fixed Lipschitz function.

In this paper, we work in the setting of Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and the harmonic function theory in this setting introduced by Muckenhoupt--Stein, especially the generalised…

We investigate $L^1(\mathbb R^n)\to L^\infty(\mathbb R^n)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there is an eigenvalue at zero energy and $n\geq 5$ is odd. In particular, we show that if there is an…

We establish the existence of ground states on Euclidean space for the Laplace operator involving the Hardy type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy…

The problem of describing the analytic functions $g$ on the unit disc such that the integral operator $T_g(f)(z)=\int_0^zf(\zeta)g'(\zeta)\,d\zeta$ is bounded (or compact) from a Banach space (or complete metric space) $X$ of analytic…

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…