@article{KATEA2026, 
author = {Rahma KATEA and Yasin KAYA},
title = {On the compactness of families of continuous functions in Grand Lebesgue spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13647-13659},
keywords = {grand Lebesgue spaces, compactness, Kolmogorov–Riesz theorem, Arzelà–Ascoli theorem, weighted function spaces, fractional Sobolev embedding},
url = {https://www.sciopen.com/article/10.3934/math.2026562},
doi = {10.3934/math.2026562},
abstract = {In this paper, we established compactness results for families of continuous functions in grand Lebesgue spaces        G    ψ  , where    ψ  :  (  a  ,  b  )  →  (  0  ,  ∞  ) is a given positive function that determines the structure of the space. In particular, we showed that equicontinuity together with uniform boundedness implies relative compactness in the        G    ψ  -norm. The approach is based on Arzelà–Ascoli-type arguments combined with uniform control in grand Lebesgue space (GLS) norms. Several examples were provided to illustrate convergence mechanisms, and extensions to weighted GLS and fractional Sobolev-type settings are discussed. These results establish a unified compactness framework in grand Lebesgue spaces and provide a foundation for further investigations in Sobolev-type embeddings and related analytical models.}
}