Some new results related to Lorentz GΓ-spaces and interpolation

• Published in: Journal of mathematical analysis and applications Vol. 483; no. 2; p. 123623
• Main Authors: Ahmed, Irshaad, Fiorenza, Alberto, Formica, Maria Rosaria, Gogatishvili, Amiran, Rakotoson, Jean Michel
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.03.2020; Elsevier
• Subjects: Classical Lorentz-spaces; Grand and Small Lebesgue spaces; Interpolation; Mathematics; Very weak solution; Interpolation; Classical Lorentz-spaces; Very weak solution; Grand and Small Lebesgue spaces
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2019.123623

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 GΓ-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 Ω with data in the space of the integrable function with respect to the distance function to the boundary of Ω.