Given an Ap-Muckenhoupt weight on a fractal obtained as the attractor of an iterated function system, we construct a sequence of approximating weights, which are simple functions belonging uniformly to the Ap class on the ...

The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p(w) are the Calderón weights of the class Cp. We prove a characterization of the weights ...

Given a space of homogeneous type (X, d, μ) and 1 < p< ∞, the main purpose of this note is to find sufficient conditions on a function w and on a subset F of X, such that w(d(x, F)) belongs to the Muckenhoupt class Ap(X, ...

In this note we prove that the Hausdorff distance between compact sets and the Kantorovich distance between measures, provide an adequate setting for the convergence of Muckenhoupt weights. The results which we prove on ...

In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes , which were extensively studied by Lerner et al. and which are the ...

We present sharp quantitative weighted norm inequalities for the Hardy- Littlewood maximal function in the context of locally compact abelian groups, obtaining an improved version of the so-called Buckley's theorem. On the ...

We present a general approach for proving the optimality of the exponents on weighted estimates. We show that if an operator T satisfies a bound like ∥ T ∥ Lp(w) ≤ c [w]βAp w ε Ap, then the optimal lower bound for β is ...

In this paper we study inequalities with weights for fractional operators Tαgiven by convolution with a kernel Kαwhich is supposed to satisfy some size condition and a fractional Hörmander type condition. As it is done for ...

A quantitative two weight theorem for the Hardy-Littlewood maximal operator is proved, improving the known ones. As a consequence, a new proof of the main results in papers by Hyt¨onen and the first author and Hyt¨onen, ...

In this paper, we study integral operators of the form, where Ai are certain invertible matrices, αi > 0, 1 ≤ i ≤ m, α1 + ... + αm = n - α, 0 ≤ α < n. For, we obtain the Lp(ℝn, wp) - Lq(ℝn,wq) boundedness for weights w in ...