Amiran Gogatishvili
Czech Acad. of Science

Some New Results Related to Lorentz GΓ-Spaces and Interpolation

We give definition of a new generalized Weighted Lorentz GΓ-spaces. Some properties of these spaces will presented. We will show that these paces are interpolation space in the sense of Peetre between classical Lorentz spaces. These spaces are obtained also from weighted Cesàro and Copson spaces by so call “symmetrisation”. We give a characterization of the interpolation space in the sense of Peetre for some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces. It happens that the result is always a GΓ- space, since this last space covers many spaces