Amiran Gogatishvili

Grants
- Function Spaces and Approximation (GA18-00580S)
  from 01/01/2018 to 31/12/2020 main investigator
- Objectives: We shall study important properties of various function spaces and operators acting on them. We shall focus on optimality of the obtained results. We shall develop new sampling algorithms that will have important applications in theory of approximation. We shall concentrate on applications of results obtained in other fields of mathematics.
- Function spaces, weighted inequalities, interpolation, integral operators, supremum operators (GA13-14743S)
  from 01/02/2013 to 31/12/2017 main investigator
- Objectives: The main objective of this project is to find easily verifiable conditions that characterize embeddings between function spaces or boundedness or compactness of linear and quasi-linear operators defined on function spaces and to apply the obtained results. We intend to depart from our results obtained in frame of our previous grants (both domestic and international) and also from results of other leading scientists, and to continue developing this fruitful research. We shall mainly use real-variable methods, results of functional analysis, interpolation and extrapolation theorems, and techniques of harmonic analysis including techniques developed or partly developed by members of the team such as discretization and antidiscretization of weighted inequalities, characterization of weighted inequalities for supremum operators, characterization of optimal partner spaces or iteration methods for characterization of higher-order Sobolev spaces. The project is a natural continuation of the project 201/08/0383.
- Function spaces and weighted inequalities and interpolation (201/08/0383)
  from 01/01/2008 to 31/12/2012 main investigator
- Objectives: The main goal of this project is to find easily verifiable conditions which characterize embeddings of function spaces and boundedness of linear and quasilinear operators acting between function spaces, and to apply obtained results in the theory of real interpolation. The problems we propose to be studied are central to Mathematical Analysis, in particular in the study of PDE’s, integral operators, function spaces, and the real interpolation. In addition to their intrinsic interest and importance they underpin much of the work in subjects as diverse as Fluid Mechanics and Mathematical Physics. They involve techniques which have been developed a great deal during the last decade and the members of our grant group have taken part in their development. The participants of the grant project published a number of important results in the field of function spaces in well-known academic journals.
- Function spaces and weighted inequalities for integral operators (201/05/2033)
  from 01/01/2005 to 31/12/2007 main investigator
- The main goal of this project is to find easily verifiable conditions which characterize embeddings of function spaces and boundedness of linear and quasilinear operators acting between function spaces, and to apply obtained results in the theory of real interpolation. The problems we propose to be studied are central to Mathematical Analysis, in particular in the study of PDE's, integral operators, function spaces, and the real interpolation. In addition to their intrinsic interest and importance they underpin much of the work in subjects as diverse as Fluid Mechanics and Mathematical Physics. They involve techniques which have been developed a~great deal during the last decade and the members of our grant group have taken part in their development. The participants of the grant project published a~number of important results from the given field in well-known academic journals.
- Function spaces and weighted inequalities for integral operators (201/01/0333)
  from 01/01/2001 to 31/12/2003 main investigator