Functional Analysis and Applications Seminar 

10/05/2013, 14:30 — 15:30 — Room P3.10, Mathematics Building
Stefan Samko, Universidade do Algarve and CEAF

Morrey spaces and Stummel classes

We prove a new property of Morrey function spaces: local Morrey type behaviour of functions is very close to weighted behaviour. More precisely, generalized local Morrey spaces are embedded between weighted Lebesgue spaces with weights differing only by a logarithmic factor. This leads to the statement that the generalized global Morrey spaces are embedded between two generalized Stummel classes whose characteristics similarly differ by a logarithmic factor. We give examples proving that these embeddings are strict. For the generalized Stummel spaces we also give an equivalent norm.