On the relationships between the norms of operators with endpoint singularities in Lebesgue and Hölder spaces with weight

Abstract

We select a special class of operators with endpoint singularities was found. For these operators we establish inequalities connecting the norms in Lebesgue spaces with weight and in H¨older spaces with weight. We describe specific types of operators satisfying the conditions of the main theorem on the relationship between the norms. These results can be used to study the operators acting on H¨older spaces with weight on the basis of the well-known results for operators acting on Lebesgue spaces with weight.