The paper is devoted to some problems concerning a convergence of pointwise type in the $L_2$-space over a von Neumann algebra M with a faithful normal state Φ [3]. Here $L_2=L_2(M,\Phi )$ is the completion of M under the norm ${x\to \left|x\right|}^2=\Phi {(x*x)}^{1/2}$.

The space Weak H¹ was introduced and investigated by Fefferman and Soria. In this paper we characterize it in terms of wavelets. Equivalence of four conditions is proved.

We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.

The main aim of this paper is to prove that the maximal operator ${\sigma }^{}$ is bounded from the Hardy space $H_{1/2}$ to weak-$L_{1/2}$ and is not bounded from $H_{1/2}$ to $L_{1/2}$.

Let $L$ be a non-negative self-adjoint operator acting on $L^2\left({ℝ}^n\right)$ satisfying a pointwise Gaussian estimate for its heat kernel. Let $w$ be an $A_r$ weight on ${ℝ}^n\times {ℝ}^n$, $1<r<\infty$. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H_{L,w}^p({ℝ}^n\times {ℝ}^n)$, $0<p\le 1$ associated to $L$. Based on the atomic decomposition, we show the dual relationship between $H_{L,w}^1({ℝ}^n\times {ℝ}^n)$ and ${\mathrm{BMO}}_{L,w}({ℝ}^n\times {ℝ}^n)$.

The aim of these pages is to give the reader an idea about the first part of the mathematical life of José Luis Rubio de Francia.

In this paper, the authors establish the phi-transform and wavelet characterizations for some Herz and Herz-type Hardy spaces by means of a local version of the discrete tent spaces at the origin.

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....

On estime la croissance à l’infini, en norme $L^p$, des sommes trigonométriques dont les fréquences (fixes) sont proches d’entiers (la norme $L^p$ est calculée sur un intervalle de longueur fixe dont le centre tend vers l’infini).

We consider sets in the real line that have Littlewood-Paley properties LP(p) or LP and study the following question: How thick can these sets be?