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

SEKİN Ç.

Turkish Journal of Mathematics, cilt.50, sa.2, ss.265-280, 2026 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.55730/1300-0098.3650
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.265-280
  • Anahtar Kelimeler: beta-semigroup, Biparametric potentials, Laplace-Bessel differential operator, modified Bessel potentials, modified Flett Potentials
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.