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arXiv · 1709.05892

Characterization of interpolation between Grand, small or classical Lebesgue spaces

Aberto Fiorenza·Maria Rosaria Formica·Amiran Gogatishvili·Tengiz Kopaliani·Jean Michel Rakotoson
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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 $G\Gamma$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Log}\, L)^\beta$, 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.

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Aberto Fiorenza, Maria Rosaria Formica, Amiran Gogatishvili, Tengiz Kopaliani, Jean Michel Rakotoson. 2017-09-18. Characterization of interpolation between Grand, small or classical Lebesgue spaces. https://arxiv.org/abs/1709.05892

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