Embedding functions and their role in interpolation theory. (1996) - Pustylnik, Evgeniy
Abstract : The embedding functions of an intermediate spaceA into a Banach couple( A 0, A 1 ) are defined as its embedding constants into the couples( 1 α A 0, 1 β A 1 ), ∀ α, β > 0 . Using these functions, we study properties and interrelations of different intermediate spaces, give a new description of all real interpolation spaces, and generalize the concept of weak-type interpolation to any Banach couple to obtain new interpolation theorems.