Extrapolation Theory With Applications

In the last few decades, interpolation theory has become an established field with many interesting applications to classical and modern analysis. In this book, the authors develop a general theory of extrapolation spaces, which is a complement to the familiar theory of interpolation spaces. Their results allow an extension of the classical extrapolation theorem of Yano to scales of Banach spaces. They give applications to classical and modern analysis, including extreme forms of Sobolev imbedding theorems, rearranging inequalities for classical operators, and Nash-Moser implicit function theorems.

The - and - methods; Extrapolation of real interpolation spaces; Some extensions: quasi-Banach spaces and modulars; Examples and applications; Monotonicity and local factorization; A general extrapolation principle.