Products of Functions in BMO(chi) and H-at(1)(chi) via Wavelets Over Spaces of Homogeneous Type

摘要

Let be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hytonen, the authors prove that the product of and , viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from into and from into , which affirmatively confirms the conjecture suggested by A. Bonami and F. Bernicot (This conjecture was presented by Ky in J Math Anal Appl 425:807-817, 2015).