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

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

References

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