Spectral perturbation theory and the two weights problem

Abstract

The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs of weights. We show that Koosis' 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' model provides an operator-valued version of Koosis' theorem.

14 pages, Latex

References in corpus (3)

• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II
• Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures
• Scattering theory and Banach space valued singular integrals