Regularity Properties and Lipschitz Spaces Adapted to High-Order Schrödinger Operators

Wei Chen and Chao Zhang
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Wei Chen: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
Chao Zhang: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Mathematics, 2022, vol. 10, issue 15, 1-21

Abstract: Let be the high-order Schrödinger operator ( − Δ ) 2 + V 2 , where V is a non-negative potential satisfying the reverse Hölder inequality ( R H q ), with q > n / 2 and n ≥ 5 . In this paper, we prove that when 0 < α ≤ 2 − n / q , the adapted Lipschitz spaces Λ α / 4 L we considered are equivalent to the Lipschitz space C L α associated to the Schrödinger operator L = − Δ + V . In order to obtain this characterization, we should make use of some of the results associated to ( − Δ ) 2 . We also prove the regularity properties of fractional powers (positive and negative) of the operator ℒ, Schrödinger Riesz transforms, Bessel potentials and multipliers of the Laplace transforms type associated to the high-order Schrödinger operators.

Keywords: heat semigroup; high-order Schrödinger operators; Lipschitz Hölder Zygmund spaces; Hölder estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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