We develop a general theory of extrapolation spaces, a complement to the familiar
theory of interpolation spaces. Our results allow us to extend the classical extrapolation
theorem of Yano to scales of Banach spaces. We give applications to classical and modern
analysis including extreme forms of Sobolev imbedding theorems, rearrangement
inequalities for classical operators, and Nash—Moser implicit function theorems.
Key words and phrases. Interpolation theory. Imbedding theorems. Rearrangement
Received by the Editors March 16, 1990. The first author was partially supported
by NSF grant DMS—8604528. The second author was partially supported by an
FAU Summer Research Fellowship.