### Sharp Estimates for Commutators of Singular Integrals via Iterations of the Hardy-Littlewood Maximal Function.

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We prove sharp weighted inequalities of the form $${\int}_{{\mathbf{R}}^{n}}|f\left(x\right){|}^{p}v\left(x\right)dx\le C{\int}_{{\mathbf{R}}^{n}}|q\left(D\right)\left(f\right)\left(x\right){|}^{p}N\left(v\right)\left(x\right)dx$$ where $q\left(D\right)$ is a differential operator and $N$ is a combination of maximal type operator related to $q\left(D\right)$ and to $p$.

The main purpose of this paper is to use some of the results and techniques in [9] to further investigate weighted norm inequalities for Hardy-Littlewood type maximal operators.

This paper deals with the robust stabilization of a class of nonlinear switched systems with non-vanishing bounded perturbations. The nonlinearities in the systems satisfy a quasi-Lipschitz condition. An observer-based linear-type switching controller with quantized and sampled output signal is considered. Using a dwell-time approach and an extended version of the invariant ellipsoid method (IEM) sufficient conditions for stability in a practical sense are derived. These conditions are represented...

We give ${A}_{p}$ type conditions which are sufficient for two-weight, strong $(p,p)$ inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function ${g}_{\lambda}^{*}$. Our results extend earlier work on weak $(p,p)$ inequalities in [13].

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted ${L}^{p}$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights (u,Su) where u is an arbitrary nonnegative function and S is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights (u,v) for the operators to be bounded from ${L}^{p}\left(v\right)$ to...

One of the main results in modern harmonic analysis is the extrapolation theorem of J. L. Rubio de Francia for A weights. In this paper we discuss some recent extensions of this result. We present a new approach that, among other things, allows us to obtain estimates in rearrangement-invariant Banach function spaces as well as weighted modular inequalities. We also extend this extrapolation technique to the context of A weights. We apply the obtained results to the dyadic square function. Fractional...

En esta nota se presenta en primer lugar una introducción autocontenida a la cohomología de álgebras de Lie, y en segundo lugar algunas de sus aplicaciones recientes en matemáticas y física.

In this paper, the problem of inference with misclassified multinomial data is addressed. Over the last years there has been a significant upsurge of interest in the development of Bayesian methods to make inferences with misclassified data. The wide range of applications for several sampling schemes and the importance of including initial information make Bayesian analysis an essential tool to be used in this context. A review of the existing literature followed by a methodological discussion is...

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