Related papers: Rubio de Francia Extrapolation Theorems for Quasi-…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

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 $L^\infty$…

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.

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 $u$…

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…

In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent…

We give an extension of Rubio de Francia's extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an $m$-(sub)linear operator…

In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type spaces in terms of various commutators of parabolic…

We present a multi-variable extension of Rubio de Francia's restricted weak-type extrapolation theory that does not involve Rubio de Francia's iteration algorithm; instead, we rely on the following Sawyer-type inequality for the weighted…

In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes $A_{\vec{p}}$, which were extensively studied by Lerner et al. and which are the natural…

We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Cobos-Fern\'{a}ndez-Cabrera-Mart\'{i}nez theorem. Then, as an…

We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. The linear…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

We prove fractional Leibniz rules and related commutator estimates in the settings of weighted and variable Lebesgue spaces. Our main tools are uniform weighted estimates for sequences of square-function-type operators and a bilinear…

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…

In this work we study boundedness of Littlewood-Paley-Stein square func- tions associated to multilinear operators. We prove weighted Lebesgue space bounds for square functions under relaxed regularity and cancellation conditions that are…

In this paper, we introduce anisotropic mixed-norm Herz spaces $\dot K_{\vec{q}, \vec{a}}^{\alpha, p}(\mathbb R^n)$ and $K_{\vec{q}, \vec{a}}^{\alpha, p}(\mathbb R^n)$ and investigate some basic properties of those spaces. Furthermore,…

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…

We prove the boundedness of a smooth bilinear Rubio de Francia operator associated with an arbitrary collection of squares (with sides parallel to the axes) in the frequency plane\[\left(f, g \right)\mapsto \left( \sum\_{\omega \in…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…