Quantitative Weighted Bounds for Littlewood-Paley Functions Generated by Fractional Heat Semigroups Related with Schrödinger Operators

Let L=−Δ+V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHqℝn with q>n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the qua...

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Bibliographic Details
Published in:Journal of function spaces 2023, Vol.2023, p.1-16
Main Authors: Yang, Li, Li, Pengtao
Format: Article
Language:English
Subjects:
Estimates
Harmonic analysis
Heat
Mathematical functions
Operators (mathematics)
Partial differential equations
Semigroups
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Summary:Let L=−Δ+V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHqℝn with q>n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood-Paley functions generated by fractional heat semigroups related with the Schrödinger operators.
ISSN:2314-8896
2314-8888
DOI:10.1155/2023/8001131