Multiresolution Approximations and Unconditional Bases on Weighted Lebesgue Spaces on Spaces of Homogeneous Type
Abstract
Starting from a slight modification of the dyadic sets introduced by M. Christ in [M. Christ, 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 H controled by the quasi distance d, can be constructed in this general setting in such a way that H is an orthonormal basis for L2(dµ). This paper is devoted
to explore under which conditions on the measure measure nu, the system H is also an unconditional basis for the Lebesgue spaces Lp(dnu). As a consequence, we obtain a characterization of these spaces in terms of the H–coefficients.
to explore under which conditions on the measure measure nu, the system H is also an unconditional basis for the Lebesgue spaces Lp(dnu). As a consequence, we obtain a characterization of these spaces in terms of the H–coefficients.