Related papers: Variable Martingale Hardy Spaces and Their Applica…

Last years there was increasing an interest to the so called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de…

Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…

Let $\Omega$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partial\Omega$) and define a Hardy space by imposing the non-tangential maximal…

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…

We establish some local and global well-posedness for Hartree-Fock equations of $N$ particles (HFP) with Cauchy data in Lebesgue spaces $L^p \cap L^2 $ for $1\leq p \leq \infty$. Similar results are proven for fractional HFP in…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert \sigma _{k}F\right\vert/A^2_k\right)$ of Fej\'er means of Walsh-Fourier series and prove that the it is bounded from the…

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…

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Fej\'er means in terms of the modulus of continuity on the Hardy spaces $H_{p},$ when $0<p\leq 1/2.$

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…

This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \infty$). In particular, we uncover some estimates concerning the OPAs of degree zero and one. It is also shown that if…

The main purpose of this paper is to give an estimate for the Fourier Laguerre transform on Hardy spaces in the setting of Laguerre hypergroup. The atomic and molecular characterization is investigated which allows us to prove a version 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…

We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one…

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue…

We study $l^p$ operator norms of factorable matrices and related results. We give applications to $l^p$ operator norms of weighted mean matrices and Copson's inequalities. We also apply the method in this paper to study the best constant in…

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…

In this paper we first study the generalized weighted Hardy spaces $H^p_{L,w}(X)$ for $0<p\le 1$ associated to nonnegative self-adjoint operators $L$ satisfying Gaussian upper bounds on the space of homogeneous type $X$ in both cases of…

We introduce a new ladder of function spaces which is shown to fill in the gap between the weak $L^{p\infty}$ spaces and the larger Morrey spaces, $M^p$. Our motivation for introducing these new spaces, denoted $\V^{pq}$, is to gain a more…

The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and…