Jesús Miguel Bastero Eleizalde

An explicit expression for the Kr functionals of interpolation between Lp spaces

When dealing with interpolation spaces by real methods one is lead to compute (or at least to estimate) the K-functional associated to the couple of interpolation spaces. This concept was first introduced by J. Peetre (see [8], [9]) and some efforts have been done to find explicit expressions of it for the case of Lebesgue spaces. It is well known that for the couple consisting of L1 and L8 on [0, 8) K is given by K (t; f, L1, L8) = ?0t f* where f* denotes the non increasing rearrangement of the function f. The aim of this paper is to answer a question raised by J. Peetre to the autors and to extend the results in [1] and [7] for the more general case of the Kr funcitionals between Lp spaces.