Related papers: Atomic decomposition for Morrey-Lorentz spaces

The Hardy-Morrey spaces related to Laplace-Bessel differential equations are introduced in terms of maximal functions. The atomic decomposition theory which has the same cancellation properties of the…

In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals…

The theory of tent spaces on $\mathbb{R}^n$ was introduced by Coifman, Meyer and Stein, including atomic decomposition, duality theory and so on. Russ generalized the atomic decomposition for tent spaces to the case of spaces of homogeneous…

In this article we study atomic and molecular decompositions in $2$-microlocal Besov and Triebel--Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the…

In this work, we propose an atomic decomposition of the Bergman-Orlicz spaces on the complex upper half-plane. Using this result, we characterize Carleson embeddings with loss between Bergman-Orlicz spaces and certain Orlicz spaces. We also…

We prove up to the boundary regularity estimates in Morrey-Lorentz spaces for weak solutions of the linear system of differential forms with regular anisotropic coefficients \begin{equation*} d^{\ast} \left( A d\omega \right) +…

In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilation in ${\Bbb R}^n$. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.

The purpose of this paper is to obtain atomic decomposition characterization of the weighted local Hardy space $h_{\omega}^{p}(\mathbb {R}^{n})$ with $\omega\in A_{\infty}(\mathbb {R}^{n})$. We apply the discrete version of Calder\'on's…

In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy…

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincar\'e inequality, the space $\Mone$, defined by Haj{\l}asz, is identified with a Hardy-Sobolev…

In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the Hardy type spaces X^k(M), introduced in a previous paper of the authors, have an atomic…

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…

Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are three versions of Orlicz--Morrey spaces, i.e: Nakai's (2004), Sawano--Sugano--Tanaka's (2012), and…

In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient…

We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…

A new proof is given of the atomic decomposition of Hardy spaces Hp, in the classical setting of Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general setting and non classical settings.

We provide a large family of atoms for Bergman spaces on irreducible bounded symmetric domains. This vastly generalizes results by Coifman and Rochberg from 1980. The atomic decompositions are derived using the holomorphic discrete series…

We introduce a new class of weighted local approximate atoms including classical weighted local atoms. Then we further obtain the weighted local approximate atomic decompositions of weighted local Hardy spaces $h_{\omega} ^p(R^n)$ with…

In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…

We prove an atomic type decomposition for the noncommutative martingale Hardy space $\h_p$ for all $0<p<2$ by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weak…