We investigate a scale of -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with --estimates, and arrives at --estimates, or more generally, at estimates between K-functionals from interpolation theory.
We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the -continuity property of these operators over Sobolev-type spaces of periodic functions.
On montre que les fonctions qui opèrent, par composition a gauche, sur l’espace de Besov d’exposant , avec , dans l’espace euclidien de dimension , sont précisément les fonctions lipschitziennes.