Reiteration formulae for the real interpolation method including L or R limiting spaces

TL;DR

This paper develops reiteration formulae for real interpolation spaces involving L and R limiting spaces, with applications to Lorentz spaces, enhancing understanding of limiting cases in interpolation theory.

Contribution

It introduces new reiteration formulae that include L and R limiting spaces, expanding the theoretical framework of real interpolation methods.

Findings

Reiteration formulae for limiting interpolation spaces derived

Applications to grand and small Lorentz spaces demonstrated

Enhanced understanding of limiting cases in interpolation theory

Abstract

We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so called $L$ or $R$ limiting interpolation spaces. These spaces arise naturally in reiteration formulae for the limiting cases $\theta = 0$ or $\theta = 1$. Applications to grand and small Lorentz spaces are given.