Related papers: Variable Hardy Spaces

For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Let $L=-\Delta +V$, $V\geq 0$, be the Dunkl--Schr\"odinger operator on $\mathbb R^N$. Assume that there…

Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator…

In the present paper, we investigate in Dunkl analysis, the action of some fundamental operators on the atomic Hardy space H1.

We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure \mu. The metric measure space V,d,\mu) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces…

We study the behaviour of Hardy-weights for a class of variational quasi-linear elliptic operators of $p$-Laplacian type. In particular, we obtain necessary sharp decay conditions at infinity on the Hardy-weights in terms of their…

We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal…

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…

Let $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the globally $\log$-H\"older continuous condition and $L$ a non-negative self-adjoint operator on $L^2(\mathbb R^n)$ whose heat kernels satisfying the Gaussian…

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…

We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…

We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in…

We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of weighted Hardy-Orlicz spaces, when the Orlicz function…

We introduce grand Morrey spaces and establish the boundedness of Hardy--Littlewood maximal, Calder\'on--Zygmund and potential operators in these spaces. In our case the operators and grand Morrey spaces are defined on quasi-metric measure…

Topological Ramsey spaces are spaces which support infinite dimensional Ramsey theory similarly to the Ellentuck space. Each topological Ramsey space is endowed with a partial ordering which can be modified to a $\sigma$-closed `almost…

This paper is served as a first contribution regarding the boundedness of Hausdorff operators on function spaces with smoothness. The sharp conditions are established for boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$. As…

We prove nontangential and radial maximal function characterizations for Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only…

Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition.…

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds…