INVESTIGADORES
RAMSEYER Mauricio Javier
congresos y reuniones científicas
Título:
Lipschitz spaces and the fractional integral in the context of the variable Lebesgue space L^{p(·)}
Autor/es:
MAURICIO RAMSEYER
Lugar:
Sevilla
Reunión:
Workshop; Harmonic Analysis, Metric Spaces and Applications to P.D.E.; 2011
Institución organizadora:
Instituto de Matemática de la Universidad de Sevilla
Resumen:
In recent years, function spaces with variable exponent and related differential equations have attracted the attention of many researchers.In this context, we study the fractional integral operator I_{\alpha} and its relation to certain variable Lipschitz spaces.\\For a measurable function p: R^n --> (1,\infty) (called the exponent), we consider L^{p(·)} with Luxemburg norm and introduce the associated space \mathfrak{L}_{\alpha,p(·)} where 0 < \alpha < n.\\For a certain range of values of the exponent, I_{\alpha} is not defined.In such cases, we prove that this operator can be extended to a bounded linear operator \tilde{I}_{\alpha} from L^{p(·)} into \mathfrak{L}_{\alpha,p(·)}.