Some Remarks on Integral Operators in Banach Function Spaces and Representation Theorems in Banach-Sobolev Spaces

Year 2024, Volume: 14 Issue: 2, 189 - 204, 31.07.2024

Eminaga M. Mamedov Natavan P. Nasibova Yonca Sezer

Abstract

In this paper, we consider convolution operators, integral operators with
weak singularity, Riesz potentials, in particular, those with kernels Ki (x, y) = xi−yi|x−y|n
acting in special classes of Banach function spaces X (Ω) and their subspaces Xs (Ω)), 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.

Keywords

Banach function space , rearrangement-invariant space , additive-invariant , Sobolev space , integral operator , weak singularity , Riesz potential

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