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 L∞ on [0, ∞) K is given by K (t; f, L1, L∞) = ∫0 t 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.
@article{urn:eudml:doc:41677,
title = {An explicit expression for the Kr functionals of interpolation between Lp spaces.},
journal = {Publicacions Matem\`atiques},
volume = {35},
year = {1991},
pages = {97-117},
mrnumber = {MR1103609},
zbl = {0845.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41677}
}
Bastero, Jesús; Raynaud, Yves; Rezola, M. Luisa. An explicit expression for the Kr functionals of interpolation between Lp spaces.. Publicacions Matemàtiques, Tome 35 (1991) pp. 97-117. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41677/