On a measure of non-compactness for singular integrals (Q1885166)

Summary: It is proved that there exists no weight pair \((v,w)\) for which a singular integral operator is compact from the weighted Lebesgue space \(L^p_w(R^n)\) to \(L^p_v(R^n)\). Moreover, a measure of non-compactness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.