# Some new results related to Lorentz G-gamma spaces and interpolation

## TL;DR

This paper computes the K-functional for certain space couples, enabling the determination of interpolation spaces as G-gamma spaces, with applications to regularity estimates for weak solutions of linear equations.

## Contribution

It provides explicit K-functional computations for Lebesgue and Lorentz-Marcinkiewicz spaces, extending previous results and characterizing interpolation spaces as G-gamma spaces.

## Key findings

- Interpolation spaces are G-gamma spaces covering many classical spaces.
- Explicit K-functional formulas are derived for specific space couples.
- Results facilitate regularity estimates for weak solutions of PDEs.

## Abstract

We compute the K-functional related to some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of the previous works of the authors. This computation allows to determine the interpolation space in the sense of Peetre for such couple. It happens that the result is always a G-gamma space, since this last space covers many spaces. The motivations of such study are various, among them we wish to obtain a regularity estimate for the so called very weak solution of linear equation in a domain Omega with data in the space of the integrable function with respect to the distance function to the boundary of Omega.