On a measure of non-compactness for singular integrals

Abstract

It is proved that there exists no weight pair (v, w) for which a singular integral operator is compact from the weighted Lebesgue space Lwp(Rn) to Lvp(Rn). Moreover, a measure of non-compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.