Some new results related to Lorentz G Gamma-spaces and interpolation

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 [11]. 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 a 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. (C) 2019 Elsevier Inc. All rights reserved.