Seminario Dottorato: Interpolation properties of Morrey-type spaces and their application

Wednesday 10 April 2013 h. 15:00 - room 2BC30 - Diana Darbayeva K.

ARGOMENTI: Seminars Ph.D. Program

Wednesday 10 April 2013 h. 15:00, room 2BC/30

Diana Darbayeva K. (Dip. Mat. Padova and Univ. Astana)
"Interpolation properties of Morrey-type spaces and their application"

It is well known that in the theory of partial differential equations, alongside with weighted Lebesque spaces, Morrey-type spaces and their generalizations also play an important role. Our purpose is the introduction of some generalized Morrey-type spaces, which include classical Morrey spaces, and study their properties. We give examples. Moreover, in this talk we describe the interpolation theory of linear operators and consider some applications. We present a Marcinkiewicz-type interpolation theorem for generalized Morrey-type spaces. This theorem is then applied to obtain a Young-O'Neil-type inequality for the convolution operator in the generalized Morrey-type spaces, in particular in Morrey spaces. Moreover, we also present some open problems.

Rif. int. C. Marastoni, T. Vargiolu