On the relationships between the norms of operators with endpoint singularities in Lebesgue and Hölder spaces with weight
Ukr. Mat. Zh. - 2017. - 69, № 3. - pp. 397-406
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.
Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1557-1568
We consider functional operators with shift in weighted Hölder spaces. The main result of the work is the proof of the conditions of invertibility for these operators. We also indicate the forms of the inverse operators. As an application, we propose to use these results for the solution of equations with shift encountered in the study of cyclic models for natural systems with renewable resources.