On the Relationships Between the Norms of Operators with Endpoint Singularities in Lebesgue and Hölder Spaces with Weight

Abstract

We select a class of operators with endpoint singularities. For these operators, we establish inequalities connecting the norms in Lebesgue spaces with weight with the norms in Holder spaces with weight. We describe specific types of the operators satisfying the conditions of the main theorem on relationship between the norms. The obtained results can be used to study the operators acting in Holder spaces with weight on the basis of the well-known results obtained for the operators acting upon the Lebesgue spaces with weight.