In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\G$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}(\Log L)^\beta$, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that $ 1<a<\infty, \beta \not= 0$. The method consists in computing the so called K-functional of the interpolation space and in identifying the associated norm.
Characterization of interpolation between Grand, small or classical Lebesgue spaces / Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Kopaliani, Tengiz; Rakotoson, Jean Michel. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 177:part B(2018), pp. 422-453. [10.1016/j.na.2017.09.005]
Characterization of interpolation between Grand, small or classical Lebesgue spaces
Fiorenza, Alberto;Formica, Maria Rosaria;
2018
Abstract
In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\G$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}(\Log L)^\beta$, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that $ 1I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.