We continue an investigation started in a preceding paper. We discuss the classical results of Carleson connecting Carleson measures with the -equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution of the -equation, which satisfies simultaneously a good estimate and a good estimate. This appears as a special case of our main result which can be stated as follows: Let be any measure space. Consider a bounded operator . Assume that on one hand admits an extension bounded with norm , and on the other hand that admits an extension bounded with norm . Then admits an extension which is bounded simultaneously from into and from into and satisfies
where is a numerical constant.
Cite this article
Gilles Pisier, Interpolation between Spaces and non-commutative generalizations, II. Rev. Mat. Iberoam. 9 (1993), no. 2, pp. 281–291DOI 10.4171/RMI/137