2018
DOI: 10.7153/jmi-2018-12-60
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Fractional integral associated with Schrödinger operator on vanishing generalized Morrey spaces

Abstract: Let L = − + V be a Schrödinger operator, where the non-negative potential V belongs to the reverse Hölder class RH n/2 , let b belong to a new BMO θ (ρ) space, and let I L β be the fractional integral operator associated with L . In this paper, we study the boundedness of the operator I L β and its commutators [b,I L β ] with b ∈ BMO θ (ρ) on generalized Morrey spaces associated with Schrödinger operator M α,V p,ϕ and vanishing generalized Morrey spaces associated with Schrödinger operator V M α,V p,ϕ . We fin… Show more

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Cited by 3 publications
(2 citation statements)
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“…This fact is perfectly justified by the dimensionality of the constant ε that we have clarified at the beginning of this section. From Figure 2, we see a plot of the solution (24) under the structural condition for the equation k 2 = k 1 − 3, when k 1 = 3 2 . The novelty of this work lies in the fact that the application of Lie symmetry analysis is being made for the first time, to the best of our knowledge, in such systems that lend themselves to a double interpretation in two different contexts of the applied sciences.…”
Section: Remarkmentioning
confidence: 99%
See 1 more Smart Citation
“…This fact is perfectly justified by the dimensionality of the constant ε that we have clarified at the beginning of this section. From Figure 2, we see a plot of the solution (24) under the structural condition for the equation k 2 = k 1 − 3, when k 1 = 3 2 . The novelty of this work lies in the fact that the application of Lie symmetry analysis is being made for the first time, to the best of our knowledge, in such systems that lend themselves to a double interpretation in two different contexts of the applied sciences.…”
Section: Remarkmentioning
confidence: 99%
“…V is a nonnegative potential belonging to the reverse Hölder class B n , that is, the class of all nonnegative locally L n integrable functions V(x) on R n , for which there exists C > 0 such that the reverse Hölder inequality; We mention [24], where the authors recently studied fractional integrals associated with Schrödinger operators in the framework of vanishing generalized Morrey spaces and [25], where the authors investigated the action of commutator of fractional integral with Lipschitz functions with Schrödinger operator on local generalized Morrey space.…”
Section: Introductionmentioning
confidence: 99%