In this paper, we consider convolution operators, integral operators with weak singularity, Riesz potentials, in particular, those with kernelsacting in special classes of Banach function spaces X () and their subspaces X s ()), and we prove some representation theorems for the functions from Banach-Sobolev spaces.We also prove the boundedness of Riesz potential in additive-invariant spaces.
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Mamedov et al. (2024) studied this question.