In this paper we introduce Bessel potentials and the Sobolev potential spaces resulting from them in the context of Ahlfors regular metric spaces. The Bessel kernel is defined using a Coifman type approximation of the ...

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 ...

We use Ahlfors' definition of Schwarzian derivative for curves in euclidean spaces to present new results about Mobius or projective parametrizations. The class of such parametrizations is invariant under compositions with ...

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 ...

Let μ be a non-negative Ahlfors n-dimensional measure on Rd. In this context we shall consider convolution type operators Tαf = Kα ∗f, 0 <α< n, where the kernels Kα are supposed to satisfy certain size and regularity ...

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, ...

La tesis tiene por objeto central el análisis de difusiones no locales en espacios métricos de medida, que incluyen el contexto euclídeo clásico, variedades, fractales, conjuntos discretos y otras estructuras generales. ...

We extend previous results for parametrized curves in euclidean space to be simple. The new condition depends as before on Ahlfors' Schwarzian and considers a conformal metric on a given interval and the new diameter. We ...

We study a recent general criterion for the injectivity of the conformal immersion of a Riemannian manifold into higher dimensional Euclidean space, and show how it gives rise to important conditions for Weierstrass-Enneper ...