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

Mamedov E., Nasibova N., SEZER Y.

Azerbaijan Journal of Mathematics, vol.14, no.2, pp.189-204, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.59849/2218-6816.2024.2.189
  • Journal Name: Azerbaijan Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.189-204
  • Keywords: additive-invariant, Banach function space, integral operator, rearrangement-invariant space, Riesz potential, Sobolev space, weak singularity
  • Yıldız Technical University Affiliated: Yes

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.