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 ...

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 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 ...

The classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coe cients is considered. As the period goes to zero, an asymptotic analysis of the corresponding sequence ...

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 ...

Let M be a finite von Neumann algebra with a faithful trace τ. In this paper we study metric geometry of homogeneous spaces O of the unitary group U of M, endowed with a Finsler quotient metric induced by the p-norms of ...