Strengthened Cauchy–Schwarz inequality for biorthogonal wavelets in Sobolev spaces

We prove a strengthened Cauchy–Schwarz inequality for one-dimensional biorthogonal wavelets. The functional frame is given by a class of Hilbert spaces, defined in terms of weighted Fourier transforms, which contain as relevant examples the standard Sobolev spaces H(s) as well as their homogeneous version. Intended applications concern multilevel and hierarchical methods for numerical approximation of partial differential equations.  2004 Elsevier Inc. All rights reserved