We combine dyadic analysis through Haar type wavelets defined on Christ´s families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green´s functions for fractional Laplacians on some function ...

We explore the relation of the geometric structure of the underlying space and the democratic character of Haar systems in Lorentz spaces. We show that, aside from homogeneity, some particular behavior of the space at large ...

In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601-628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453-1459, 1998) to get ...

In this work we give sufficient and necessary conditions for the boundednessof the fractional integral operator acting between weighted Orlicz spaces and suitableBMOφ spaces, in the general setting of spaces of homogeneous ...

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, μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set ...

In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for ...

Newton-Sobolev spaces, as presented by N. Shanmugalingam, describe a way to extend Sobolev spaces to the metric setting via upper gradients, for metric spaces with ´sucient´ paths of nite length. Sometimes, as is the case ...

In this note we prove that the Haar type systems defined on spaces of homogeneous type are unconditional bases for a wide family of Banach function spaces. Also, we give a characterization of these spaces via Haar coefficients. ...

We obtain a comparison of the level sets for two maximal functions on a space of homogeneous type: the Hardy-Littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the ...