Related papers: Extrapolation and Factorization
In this paper we prove the Jones factorization theorem and the Rubio de Francia extrapolation theorem for matrix $\mathcal A_p$ weights. These results answer longstanding open questions in the study of matrix weights. The proof requires the…
We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$…
In this article we give an overview of the problem of finding sharp constants in matrix weighted norm inequalities for singular integrals, the so-called matrix A2 conjecture. We begin by reviewing the history of the problem in the scalar…
We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and…
In this paper we give an overview of recent work on matrix weights, with particular emphasis on convex body sparse domination for singular integrals, Rubio de Francia extrapolation, and Jones factorization. To provide context and…
In this paper, we prove a discrete Rubio de Francia extrapolation theorem via factorization of discrete Muckenhoupt weights and discrete iterated Rubio de Francia algorithm and its duality.
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including $A_1$, $A_p$, and $A_\infty$ extrapolation in the context of Banach function…
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
In this article, we prove an analogue of the Rubio de Francia's extrapolation theorem in the setting of Hausdorff capacities. We prove the result using techniques analogous to those in the classical setting and using the recently developed…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
We prove Rubio de Francia extrapolation results in Lebesgue and grand Lebesgue spaces for quasi monotone functions with $QB_{\beta,p}$ weights. The extrapolation in Lebesgue spaces with the weight class $QB_{\beta,\infty}$ has also been…
In this paper we extend the theory of Rubio de Francia extrapolation for matrix weights, recently introduced by Bownik and the first author, to off-diagonal extrapolation. We also show that the theory of matrix weighted extrapolation can be…
This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by…
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…
These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of…
We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator are discussed: it is shown that a rotation factor is needed…