Resumen: We consider limiting real interpolation spaces defined by using powers of iterated logarithms and show
their description by means of the J -functional. Our results allow to complement some estimates on approximation
of stochastic integrals.
Resumen: We investigate the limit class of interpolation spaces that comes up by the choice θ = 0 in the definition of the real method. These spaces arise naturally interpolating by the J -method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ = 1. We also study the behavior of compact operators
under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.
Palabras clave: Extreme interpolation spaces; Real interpolation; J -functional; K-functional; Interpolation methods; Compact-Operators; Banach-Spaces; Polygons; Extrapolation; Reiteration; Duality; Mathematics
associated to polygons; Compact operators; Lorentz–Zygmund function spaces; Spaces of operators
Resumen: In a previous paper, the authors laid the foundations of a theory of Schattenñvon Neumann classes 'p
(0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional
case, it is shown that the best constant d# that relates the HilbertñSchmidt norm of a form with its bounded
norm behaves like n. Some results
are also obtained in the quasi-Banach case (0!p!1), and for twobounded
forms. Finally, the domination problem is investigated in the trilinear set-up.
