S. Beuchler : Multi-resultion weighted norm equivalences and applications
We establish multiresolution norm equivalences in weighted spaces
with possibly singular weight functions w(x) >= 0 in (0,1). Our analysis exploits the
locality of the biorthogonal wavelet basis and its dual basis functions.
The discrete norms are sums of wavelet coefficients which are weighted with
respect to the collocated weight function w within each scale.
Since norm equivalences for Sobolev norms are by now well-known, our result
can also be applied to weighted Sobolev norms. We apply our theory to
the problem of preconditioning p-Version FEM and wavelet discretizations
of degenerate elliptic problems.