Some new results related to Lorentz GΓ-spaces and interpolation

0510259 - MÚ 2021 RIV US eng J - Journal Article
Ahmed, I. - Fiorenza, A. - Formica, M. R. - Gogatishvili, Amiran - Rakotoson, J. M.
Some new results related to Lorentz GΓ-spaces and interpolation.
Journal of Mathematical Analysis and Applications. Roč. 483, č. 2 (2020), č. článku 123623. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR(CZ) GA18-00580S
Institutional support: RVO:67985840
Keywords : grand and small Lebesgue spaces * classical Lorentz-spaces * interpolation * very weak solution
OECD category: Pure mathematics
Impact factor: 1.583, year: 2020
Method of publishing: Limited access
https://doi.org/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 the previous paper. 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.
Permanent Link: http://hdl.handle.net/11104/0300775