Investigation of the behavior of biparametric potentials associated with the Laplace-Bessel differential operator in weighted Lebesgue spaces

Authors

ÇAĞLA SEKİNFollow

Author ORCID Identifier

ÇAĞLA SEKİN: 0000-0001-7176-5164

Abstract

In this article, we investigate the mapping properties of potential-type operators of the form J^α_β = (E + (−Δ_ν)^β/2)^−α/β, (β, α > 0), where Δ_ν is the Laplace-Bessel differential operator. We establish norm inequalities that describe the boundedness of the operator J^α_β from L_p,ν to L_q,ν under suitable conditions on α, β, p and q. The results extend and unify the known estimates for classical potential operators. In particular, the cases β = 1 and β = 2 correspond to the modified Flett and Bessel potentials, respectively.

DOI

10.55730/1300-0098.3650

Keywords

Biparametric potentials, modified Flett Potentials, modified Bessel potentials, Laplace-Bessel differential perator, beta-semigroup

First Page

265

Last Page

280

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

SEKİN, Ç (2026). Investigation of the behavior of biparametric potentials associated with the Laplace-Bessel differential operator in weighted Lebesgue spaces. Turkish Journal of Mathematics 50 (2): 265-280. https://doi.org/10.55730/1300-0098.3650