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 ...

Let w be an A∞-Muckenhoupt weight in R. Let L2(wdx) denote the space of square integrable real functions with the measure w(x)dx and the weighted scalar product f, g w = R f g wdx. By regularization of an unbalanced Haar ...

We give sufficient conditions on a real number β and on a closed set F in a general space of homogeneous type (X,d,μ)(X,d,μ) in such a way that μ(B(x,d(x,F)))βμ(B(x,d(x,F)))β becomes a Muckenhoupt weight. In order to prove ...

Let (X,d,mu) be an Ahlfors metric measure space. We give sufficient conditions on a closed set Fsubseteq X and on a real number eta in such a way that d(x,F)^beta becomes a Muckenhoupt weight. We give also some illustrations ...

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 ...

El desarrollo de esta tesis comienza con el estudio de promedios de Luxemburg y operadores maximales generalizados actuando sobre funciones en espacios de tipo homogéneo, así como también diversos resultados asociades con ...

We characterize the weak-type boundedness of the Hilbert transform H on weighted Lorentz spaces Lambda_p(u,w) , with p>0, in terms of some geometric conditions on the weights u and w and the weak-type boundedness of the ...

We discuss several characterizations of the A∞ class of weights in the setting of general bases. Although they are equivalent for the usual Muckenhoupt weights, we show that they can give rise to different classes of weights ...