Limiting Interpolation by Lorentz-Zygmund Spaces: Grand/Small Lebesgue, Lorentz, and Modelled Besov Spaces

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DOI: https://doi.org/10.28924/2291-8639-24-2026-98
Published: Apr 7, 2026
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Muhammad Awais, Zia Bashir, Thitiporn Linitda, Thanin Sitthiwirattham, Limiting Interpolation by Lorentz-Zygmund Spaces: Grand/Small Lebesgue, Lorentz, and Modelled Besov Spaces, Int. J. Anal. Appl., 24 (2026), 98.

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Muhammad Awais, Zia Bashir, Thitiporn Linitda, Thanin Sitthiwirattham

Abstract

In this article, we investigate limiting real interpolation spaces. Our primary goal is to thoroughly explore and establish the interpolation properties within critical cases θ = 0 and θ = 1 for Lorentz spaces, Grand and Small Lebesgue spaces as well as for Besov spaces modelled on so called Lorentz-Zygmund spaces. The key findings from our research indicate that Lorentz-Zygmund space can be viewed as an interpolation space by Peetre’s definition. This interpolation occurs between two Grand Lebesgue spaces, two Small Lebesgue spaces, or even between two Lorentz spaces.

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