Skip to main content
European Commission logo print header
Contenu archivé le 2022-12-23

Variable exponent analysis

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.

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)