Characterization of interpolation between Grand, small or classical Lebesgue spaces

0496179 - MÚ 2019 RIV GB eng J - Journal Article
Fiorenza, A. - Formica, M. R. - Gogatishvili, Amiran - Kopaliani, T. - Rakotoson, J. M.
Characterization of interpolation between Grand, small or classical Lebesgue spaces.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 177, December (2018), s. 422-453. ISSN 0362-546X. E-ISSN 1873-5215
R&D Projects: GA ČR GA13-14743S
Institutional support: RVO:67985840
Keywords : Grand Lebesgue space * small Lebesgue space * Lebesgue space * Lorentz–Zygmund space
OECD category: Pure mathematics
Impact factor: 1.450, year: 2018
https://www.sciencedirect.com/science/article/pii/S0362546X17302328?via%3Dihub

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz–Zygmund spaces or more generally GΓ-spaces. As a direct consequence of our results any Lorentz–Zygmund space La,r(Log L)β, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that 1 < a < ∞, β ̸= 0. The method consists in computing the so called K-functional of the interpolation space and in identifying the associated norm.
Permanent Link: http://hdl.handle.net/11104/0289004