Related papers: Atomic decompositions for noncommutative martingal…
We prove that atomic decomposition for the Hardy spaces h_1 and H_1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h_p and bmo form interpolation scales with…
In this paper, we introduce the notion of martingale Hardy-amalgam spaces: $ H^s_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$. We present two atomic decompositions for these spaces. The dual space of $H^s_{p,q}$ for $0<p\le q\le 1$…
We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend…
Given a probability space $(\Omega,\Sigma,\mu)$, the Hardy space $\mathrm{H}_1(\Omega)$ which is associated to the martingale square function does not admit a classical atomic decomposition when the underlying filtration is not regular. In…
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.
In this paper, we establish continuous bilinear decompositions that arise in the study of products between elements in martingale Hardy spaces $ H^p\ (0<p\leqslant 1) $ and functions in their dual spaces. Our decompositions are based on…
We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in…
For $f \in H^p(\delta^2)$, $0<p\leq 2$, with Haar expansion $f=\sum f_{I \times J}h_{I\times J}$ we constructively determine the Pietsch measure of the $2$-summing multiplication operator \[\mathcal{M}_f:\ell^{\infty} \rightarrow…
In this paper, we study the John-Nirenberg inequality for BMO and the atomic decomposition for H1 of noncommutative martingales. We first establish a crude version of the column (resp. row) John-Nirenberg inequality for all 0 < p < \infty.…
The aim of this paper is twofold. On the one hand, we manage to identify Banach-valued Hardy spaces of analytic functions over the disc $\mathbb{D}$ with other classes of Hardy spaces, thus complementing the existing literature on the…
Let $p(\cdot)$ be a measurable function defined on a probability space satisfying $0<p_-:={\rm ess}\inf_{x\in \Omega}p(x)\leq {\rm ess}\sup_{x\in\Omega}p(x)=:p_+<\infty$. We investigate five types of martingale Hardy spaces $H_{p(\cdot)}$…
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…
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 introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak type and strong type inequalities on Doob's maximal operator and…
In this article, by means of the matrix-weighted grand maximal function we first introduce the variable Hardy space $H^{p(\cdot)}_W$ on $\mathbb{R}^n$ with the $\mathscr{A}_{p(\cdot),\infty}$ matrix weight $W$ and with the variable exponent…
We constructively determine the Pietsch measure of the 2-summing multiplication operator \[\mathcal{M}_u:\ell^{\infty} \rightarrow H^p, \quad (\varphi_I) \mapsto \sum \varphi_Ix_Ih_I. \] Our construction of the Pietsch measure for the…
In this paper, we give an atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^n\times {\rr}^m)$ for $0<p\le 1$, which were introduced in \cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that these…
The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H^1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about…
In this paper, we show that every (weighted) Bergman space $\mathcal{A}^p_{\alpha} (\mathbb{B}_n)$ in the complex ball admits an atomic decomposition of real-variable type for any $0 < p \le 1$ and $\alpha > -1.$ More precisely, for each $f…
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…