Related papers: Weighted local Hardy spaces and their applications

Suppose that $(X,d,\mu)$ is a space of homogeneous type, with upper dimension $\mu$, in the sense of R. R. Coifman and G. Weiss. Let $\eta$ be the H\"{o}lder regularity index of wavelets constructed by P. Auscher and T. Hyt\"{o}nen. In this…

Given a Muckenhoupt weight $w$ and a second order divergence form elliptic operator $L$, we consider different versions of the weighted Hardy space $H^1_L(w)$ defined by conical square functions and non-tangential maximal functions…

We prove the Lorentz-Shimogaki and Boyd theorems for the spaces $\Lambda^p_u(w)$. As a consequence, we give the complete characterization of the strong boundedness of $H$ on these spaces in terms of some geometric conditions on the weights…

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…

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.

The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…

We develop a theory of capacities associated with local Muckenhoupt weights. Fundamental properties of local Muckenhoupt weights will be revisited. Weak type boundedness of nonlinear potential and capacitary strong type inequalities…

Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S.…

Let $w$ be a Muckenhoupt $A_2(\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\mathop\mathrm{div}(A\nabla)$ the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$. In this article, the authors establish the Riesz transform…

We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.

Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the…

In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad…

Let $L$ be a one-to-one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the weak Hardy space…

We define $A_{p(\cdot)}^{\rm loc}$ and show that the weighted inequality for local Hardy--Littlewood maximal operator on the Lebesgue spaces with variable exponent. This work will extend the theory of Rychkov, who developed the theory of…

In this paper, we give a complete real-variable theory of local variable Hardy spaces. First, we present various real-variable characterizations in terms of several local maximal functions. Next, the new atomic and the finite atomic…

Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ${\mathcal X}$. In this paper, the…

Let $1\leq p<\infty$, $\alpha>-1$, and let $\varphi$ be a measurable function on $(0,\infty)$. The main purpose of this paper is to study the Hausdorff operator \[ \mathscr H_\varphi f(z)=\int_0^\infty f\left(\frac{z}{t}\right)…

We give necessary and sufficient conditions for inhomogeneous Calder\'on-Zgymund operators to be bounded on the local hardy spaces $h^p(\mathbb{R}^n)$. We then give applications to local and truncated Riesz transforms, as well as…