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Project Name : New aspects in function spaces, differential and integral operators and nonlinear analysis, and applications in PDE
Donor Organization : Shota Rustaveli National Scientific Foundation
Budget: 150000 lari
Grant number : GNSF/ST09_23_3-100
Direction : 5 Mathematics, Mechanics
Subdirection : 5-100 Mathematical Analysis
Key word : Integral operators, boundary value problems
Description : The aim of the project is to investigate various problems in harmonic analysis, function spaces and nonlinear analysis appearing in different contexts but strongly interrelated in many respects: motivation, techniques and methodology. The project anticipates the research of classical problems through the nonstandard approaches specified by demands. Many of the problems to be studied concern the boundedness and compactness of various kinds of operators, such as: multilinear singular integrals, potentials, one-sided integral operators, their commutators etc. The origins of these operators can be traced in partial differential equations, in complex analysis and in approximation theory. From the beginning, harmonic analysis played a central role in many fields of mathematics and physics, by creating tools for the investigation of differential and integral operators with some invariance property. Modern harmonic analysis enlarged its scope to encompass analytical problems posed on metric (quasi-metric) measure spaces. There are various historical motivations for this development: boundary value problems for harmonic and analytic functions. Time-frequency analysis, including wavelets, comes into the picture both as a tool and as an object of study in its own right. These numerous situations, different as they may appear, are however strongly linked to each other. Members of various nodes collaborate with deep interactions on different tasks.
Duration : 22/01/2010 - up to date
Leader : Vakhtang Kokilashvili
Project manager :
Project participant(s) :
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