Objectif The project is related to such areas of Mathematics as Harmonic Analysis, Functional Analysis, Fractional Analysis, Operator Theory, Non-linear Analysis, Partial Differential Equations, Boundary Value Problems, Integral Equations. The project is based on the recent progress in the theory of Lebesgue and Sobolev spaces with variable exponent. This progress provides a possibility of successful advance in various directions. Within the project it is planned to develop both the study of variable exponent spaces themselves and the operator theory in such spaces, including the classical operators of harmonic analysis: maximal, singular and potential operators. Applications to boundary value problems of analytic and harmonic functions and to integral equations in spaces with variable exponent is also planned.The project will focus on resolution of the following main problems of the above mentioned areas of mathematics: General conditions for weighted boundedness of maximal operators in variable exponent spaces (VES); Sobolev type estimates for the Riesz potentials and one-sided potentials in weighted VES; Imbedding theorems for Sobolev type spaces with smoothness of fractional order and integrability of variable order; Mapping properties for ergodic maximal functions and Hilbert transforms in VES; Theorems for Fourier multipliers in weighted VES; Hardy spaces with variable exponent and related spaces of harmonic functions; Boundary value problems for functions in VES; Dirichlet boundary value problems for PDEs and boundary value problems for elliptic equations with non-standard growth conditions; Cesaro summability of Fourier series when the order of summability is a function; Behaviour of Fourier operators in weighted variable Lebesgue and Lorentz spaces; Application of mapping properties of integral operators to the study of Fredholmness of integral equations in variable exponent Lebesgue spaces. Mots‑clés Differential Equations & Boundary Problems Real & Functional Analysis Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Thème(s) Data not available Appel à propositions Data not available Régime de financement Data not available Coordinateur UNIVERSIDADE DO ALGARVE Contribution de l’UE Aucune donnée Adresse CAMPUS DE GAMBELAS FARO Portugal Voir sur la carte Coût total Aucune donnée Participants (3) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire A. RAZMADZE MATHEMATICAL INSTITUTE Géorgie Contribution de l’UE Aucune donnée Adresse M. ALEKSIDZE, 1 TBILISI Voir sur la carte Coût total Aucune donnée INSTITUTE OF MATHEMATICS AND MECHANICS OF AZNAS Azerbaïdjan Contribution de l’UE Aucune donnée Adresse F. AGAYEV STREET, 9 BAKU Voir sur la carte Coût total Aucune donnée UNIVERSITY OF OULU Finlande Contribution de l’UE Aucune donnée Adresse OULU Voir sur la carte Coût total Aucune donnée