Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE GENERALIZED ORNSTEIN-UHLENBECK OPERATORS WITH REGULAR AND SINGULAR POTENTIALS IN WEIGHTED Lp-SPACES

  • Imen Metoui (Laboratory of Mathematical Analysis and Applications (LMAA-LR11-ES11) Faculty of Mathematical, Physical and Natural Sciences of Tunis University of Tunis El-Manar)
  • Received : 2023.06.03
  • Accepted : 2023.07.21
  • Published : 2024.01.31
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Abstract

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials AΦ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|-2 with a suitable domain generates a quasi-contractive, positive and analytic C0-semigroup in Lp(ℝN , e-Φ(x)dx), 1 < p < ∞. The proofs are based on an Lp-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

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References

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