Resumen de Multiresolution approximations and unconditional bases on weighted Lebesgue spaces on spaces of homogeneous type

Hugo Aimar, Ana Lucía Bernardis , Bibiana Iaffei

• Starting from a slight modification of the dyadic sets introduced by M. Christ in [A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990) 601¿628] on a space of homogeneous type (X,d,µ), an MRA type structure and a Haar system controlled by the quasi distance d, can be constructed in this general setting in such a way that is an orthonormal basis for L2(dµ). This paper is devoted to explore under which conditions on the measure ?, the system is also an unconditional basis for the Lebesgue spaces Lp(d?). As a consequence, we obtain a characterization of these spaces in terms of the ¿coefficients