Related papers: Real-Variable Theory of Local Variable Hardy Space…

We show that many classical results in Hardy space theory have exact analogues when the Fourier coefficients are allowed only to be real.

In this paper, we study weighted local Hardy spaces $h^p_\wz(\rz)$ associated with local weights which include the classical Muckenhoupt weights. This setting includes the classical local Hardy space theory of Goldberg \cite{g}, and the…

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand…

Let $\Gamma$ be a graph. Under suitable geometric assumptions on $\Gamma$, we give several equivalent characterizations of Sobolev and Hardy-Sobolev spaces on $\Gamma$, in terms of maximal functionals, Haj{\l} asz type functionals or atomic…

We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results…

For a closed locally symmetric space M=\Gamma\G/K and a representation of G we consider the push-forward of the fundamental class in the homology of the linear group and a related invariant in algebraic K-theory. We discuss the…

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family ${\mathcal B}_{H}(\lambda)$ of…

One defines a non-homogeneous space $(X, \mu)$ as a metric space equipped with a non-doubling measure $\mu$ so that the volume of the ball with center $x$, radius $r$ has an upper bound of the form $r^n$ for some $n> 0$. The aim of this…

It was well known that geometric considerations enter in a decisive way in many questions of harmonic analysis. The main purpose of this paper is to provide the criterion of the boundedness for singular integrals on the Hardy spaces and as…

Let $\nu = (\nu_1, \ldots, \nu_n) \in (-1/2, \infty)^n$, with $n \ge 1$, and let $\Delta_\nu$ be the multivariate Bessel operator defined by \[ \Delta_{\nu} = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{\nu_j^2 -…

A large part of the theory of Hardy spaces on products of Euclidean spaces has been extended to the setting of products of stratified Lie groups. This includes characterisation of Hardy spaces by square functions and by atomic…

We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…

We consider local "complementary" generalized Morrey spaces ${\dual \cal M}_{\{x_0\}}^{p(\cdot),\om}(\Om)$ in which the $p$-means of function are controlled over $\Om\backslash B(x_0,r)$ instead of $B(x_0,r)$, where $\Om \subset \Rn$ is a…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour. However, there are natural examples where one finds a mix of both behaviour (locally Gaussian and…

In this paper, using the remarkable orthonormal wavelet basis constructed recently by Auscher and Hyt\"onen, we establish the theory of product Hardy spaces on spaces ${\widetilde X} = X_1\times X_2\times\cdot \cdot\cdot\times X_n$, where…

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order…

In harmonic analysis, studies of inequalities of Riesz potential in various function spaces have a very important place. Variable exponent Morrey type spaces and the examines of the boundedness of such operators on these spaces have an…