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.
