IUMJ

Title: Spectral perturbation theory and the two weights problem

Authors: Alexander Pushnitski and Alexander Volberg

Issue: Volume 63 (2014), Issue 5, 1349-1364

Abstract:

The famous two weights problem consists of characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis's theorem of 1980 gives a way to construct a certain class of pairs of weights. We show that Koosis's theorem is closely related to (in fact, is a direct consequence of) a spectral perturbation model suggested by de Branges in 1962. Further, we show that de Branges's model provides an operator-valued version of Koosis's theorem.