Alexandre Almeida
Lesbesgue spaces with variable integrability
Lebesgue spaces (and corresponding Sobolev spaces) with variable integrability have attracted attention not only by their theoretical interest but also by some applications, including image restoration and modeling of electrorheological fluids. The purpose of this talk is to survey basic properties of such spaces and to point out some issues arising when the integrability order is allowed to vary from point to point.
Anabela Silva
Factorizations for convolution type operators on variable exponent Lebesgue spaces
Variable exponent Lebesgue spaces and operators acting between them have been intensively investigated during the last years. The growing interest in such topic is already connected with several applications (e.g. in problems of fluid dynamics, elasticity theory and differential equations). In the present talk, we will consider a class of convolution type operators, the Wiener-Hopf plus Hankel operators, acting between variable exponent Lebesgue spaces on the real line. As main results, we obtain invertibility and Fredholm criteria for those operators via certain factorizations their Fourier symbols.
This is based on a joint work with L.P. Castro and is being supported by the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e a Tecnologia”), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. Anabela Silva also acknowledges the support of FCT through the postdoctoral scholarship SFRH/BPD/96763/2013.
This is based on a joint work with L.P. Castro and is being supported by the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e a Tecnologia”), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. Anabela Silva also acknowledges the support of FCT through the postdoctoral scholarship SFRH/BPD/96763/2013.