Embedding functions and their role in interpolation theory. (1996)

• Record Type: Journal Article
• Authors: Pustylnik, Evgeniy
• Is Part Of: Abstract and applied analysis. Volume 1:Number 3(1996)
• Page Start: 305
• Page End: 325
• Publication Date: 1996
• Subjects: Embedding -- interpolation -- K-space -- operator of weak type; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337596000164
• Languages: English
• ISSNs: 1085-3375

Abstract

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.