Related papers: Martingale Hardy spaces with variable exponents

We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using…

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p,p)$ and strong type $(p,p)$ inequalities for the Hardy--Littlewood maximal operators, both centered and…

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…

We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…

We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the Burkholder/Gundy and Burkholder/Rosenthal inequalities in this setting. The usual…

In this paper we introduce the generalized BMO martingale spaces by stopping time sequences, which enable us to characterize the dual spaces of martingale Hardy-Lorentz spaces $H_{p,q}^s$ for $0<p\leq1, 1<q<\infty$. Moreover, by duality we…

We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.

In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale…

We give H\"older's inequalities for integral and conditional expectation involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for the operator are established.

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…

Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition. Let $\mathcal{H}^{p(\cdot)}_A({\mathbb…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying that there exists a constant $p_0\in(0,p_-)$, where $p_-:=\mathop{\mathrm {ess\,inf}}_{x\in \mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal…

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…

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…

Let $p(\cdot):\ \mathbb{R}^n\to(0,\infty]$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition and $A$ a general expansive matrix on $\mathbb{R}^n$. Let $H_A^{p(\cdot)}(\mathbb{R}^n)$ be the variable…

This paper gives a systematic study of operator-valued local Hardy spaces. These spaces are localizations of the Hardy spaces defined by Tao Mei, and share many properties with Mei's Hardy spaces. We prove the ${\rm h}_1$-$\rm bmo$ duality,…

We investigate the class $\mathcal{B}^{loc}(\mathbb{R}^{n})$ of exponents $p(\cdot)$ for with local Hardy-Littlewood maximal operator is bounded in $L^{p(\cdot)}(\mathbb{R}^{n})$ space. Littlewood-Paley square-function characterization of…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

In this paper, we prove strong type, weak type inequalities of Hardy-Littlewood maximal operator and fractional Hardy-Littlewood maximal operator on variable sequence spaces lp(Z). This is achieved using Calderon-Zygmund decomposition for…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function and $X$ a ball quasi-Banach function space. In this paper, we first study the relationship between two kinds of variable weights…