Investigation of the behavior of biparametric potentials associated with the Laplace-Bessel differential operator in weighted Lebesgue spaces
Turkish Journal of Mathematics, vol.50, no.2, pp.265-280, 2026 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 50 Issue: 2
- Publication Date: 2026
- Doi Number: 10.55730/1300-0098.3650
- Journal Name: Turkish Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.265-280
- Keywords: beta-semigroup, Biparametric potentials, Laplace-Bessel differential operator, modified Bessel potentials, modified Flett Potentials
- Akdeniz University Affiliated: Yes
Abstract
In this article, we investigate the mapping properties of potential-type operators of the form (formula presented) where ∆ν is the Laplace-Bessel differential operator. We establish norm inequalities that describe the boundedness of the operator (formula presented) from Lp,v to Lq,v 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.