On the Noether property of linear singular integral equations in weighted Lebesgue spaces (Q581798)

The author considers the linear singular integral equation \(a\phi +bS\phi +v\phi =f,\) where \(S\phi =(\pi \cdot i)^{-1}\int_{\Gamma}\phi (\tau)(\tau -t)^{-1}d\tau,\) v a compact operator and a,b bounded measurable functions. Under general assumptions on \(\Gamma\) and the weight function w he shows that the Noether problem for this problem in the space \(L_ p(\Gamma,w)\) may be reduced to an analogous problem in the space \(L_ p(\Gamma)\) (without weight).