In this note we give sufficient conditions on two dyadic systemson a space of homogeneous type in order to obtain the equivalence of corre-sponding Haar systems on Lebesgue spaces. The main tool is the vector valuedFe ...

In this note we consider Haar type systems as unconditional bases for Lorentz spaces defined on spaces of homogeneous type. We also give characterizations of these spaces in terms of the Haar coefficients. The basic tools ...

In this note we prove that Haar type systems are unconditional basis in the generalized dyadic Hardy space HD 1 in the setting of spaces of homogeneous type. As a consequence, we obtain an alternative proof of the ...

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. ...

Este trabajo explora la relación entre la estabilidad de pequeñas perturbaciones de sistemas de Haar y la geometría del dominio de las funciones del espacio L2 subyacente. La tesis contiene aportes de la teoría de integrales ...

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 give sufficient conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these result we ...

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 ...

In this paper we solve the initial value problem for the nonlocal diffusion generated by the space fractional derivative induced by the dyadic tilings of M. Christ on a space of homogeneous type. We consider the problems ...

In this note we consider the pointwise convergence to the initial data for the solutions of some nonlocal dyadic Schrödinger equations on spaces of homogeneous type. We prove the a.e. convergence when the initial data ...