Characterization of interpolation between Grand, small or classical Lebesgue spaces

Author: Amiran Gogatishvili
Co-authors: Tengiz Kopaliani, Alberto Fiorenza, Maria Rosaria Formica, Jean Michel Rakotoson
Keywords: Grand Lebesgue space, small Lebesgue spaces, Lebesgue spaces, Lorentz-Zygmund space, real interpolation space, K -functional
Annotation:

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally G -spaces. As a direct consequence of our results any Lorentz-Zygmund space, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that The method consists in computing the so called K-functional of the interpolation space and in identifying the associated norm

Lecture files:

Characterization of interpolation between Grand, small or classical Lebesgue spaces [en]