Abstract:
Research in the field of functional spaces, operator theory and geometric analysis has been most actively conducted since the middle of the last century, influencing the general state and the possibility of applying the results of fundamental mathematical research to solving problems from related fields. In recent years, along with the classical ones, new functional classes have appeared in solving a number of modern problems, requiring non-standard approaches to study.
In this project, we will deal with weighted Lebesgue classes, Sobolev function spaces, Lizorkin-Tribel spaces, Besov spaces on irregular domains, Lorentz cones, Morry and Hertz spaces, Cesaro and Copson spaces, spaces with variable smoothness index. The analysis of these functional spaces and the operators operating in them is very relevant and far from complete. Within the framework of the project, their research will continue, new results will be obtained, new methods and approaches will be developed and existing ones will be improved.
